Prove some lemmas about transporting path_sigma

Also clean up the corresponding lemmas about path_prod
Define the dual functor [Cat -> Cat]

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8m05.62s | Total                                                             | 7m59.34s
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1m54.75s | theories/categories/Comma/ProjectionFunctors                      | 1m53.56s
0m33.15s | theories/categories/Adjoint/Composition/AssociativityLaw          | 0m34.11s
0m28.01s | theories/categories/Comma/Dual                                    | 0m28.60s
0m17.95s | theories/categories/Adjoint/UnitCounitCoercions                   | 0m16.44s
0m17.38s | theories/categories/ExponentialLaws/Law4/Functors                 | 0m17.74s
0m16.24s | theories/categories/Comma/InducedFunctors                         | 0m16.15s
0m13.83s | theories/hit/Flattening                                           | 0m13.45s
0m12.80s | theories/categories/Adjoint/Composition/Core                      | 0m12.78s
0m12.48s | theories/categories/Adjoint/Dual                                  | 0m11.86s
0m12.18s | theories/categories/Pseudofunctor/Core                            | 0m12.66s
0m11.14s | theories/categories/Pseudofunctor/FromFunctor                     | 0m10.94s
0m10.52s | theories/categories/Adjoint/Composition/IdentityLaws              | 0m10.26s
0m09.81s | theories/categories/Functor/Pointwise/Properties                  | 0m09.68s
0m08.27s | theories/categories/Functor/Prod/Universal                        | 0m08.44s
0m08.16s | theories/categories/GroupoidCategory/Morphisms                    | 0m08.41s
0m07.91s | theories/categories/ExponentialLaws/Law1/Law                      | 0m08.05s
0m07.54s | theories/hit/Connectedness                                        | 0m07.76s
0m06.88s | theories/categories/UniversalProperties                           | 0m06.68s
0m06.78s | theories/categories/Adjoint/Paths                                 | 0m06.65s
0m06.17s | theories/categories/Functor/Paths                                 | 0m06.22s
0m05.82s | theories/categories/Functor/Sum                                   | 0m05.82s
0m05.71s | theories/categories/Adjoint/UnitCounit                            | 0m05.88s
0m05.69s | theories/categories/Category/Morphisms                            | 0m05.95s
0m05.61s | theories/categories/DualFunctor                                   |   N/A
0m04.93s | theories/EquivalenceVarieties                                     | 0m05.06s
0m04.90s | theories/categories/ExponentialLaws/Law2/Functors                 | 0m04.97s
0m04.08s | theories/categories/Category/Sigma/OnMorphisms                    | 0m04.08s
0m03.66s | theories/categories/ProductLaws                                   | 0m03.54s
0m03.53s | theories/types/ObjectClassifier                                   | 0m03.98s
0m03.02s | theories/categories/Adjoint/UniversalMorphisms                    | 0m02.77s
0m03.00s | theories/types/Sigma                                              | 0m03.12s
0m02.86s | theories/categories/Functor/Prod/Functorial                       | 0m02.73s
0m02.68s | theories/Equivalences                                             | 0m02.62s
0m02.63s | theories/categories/FunctorCategory/Functorial                    | 0m02.65s
0m02.29s | theories/categories/Category/Sum                                  | 0m02.18s
0m02.22s | theories/categories/Functor/Attributes                            | 0m02.16s
0m02.19s | theories/categories/Comma/Core                                    | 0m02.07s
0m01.98s | theories/categories/Category/Sigma/Core                           | 0m02.16s
0m01.87s | theories/PathGroupoids                                            | 0m01.84s
0m01.86s | theories/categories/NaturalTransformation/Dual                    | 0m01.82s
0m01.76s | theories/categories/HomFunctor                                    | 0m01.90s
0m01.76s | theories/categories/NaturalTransformation/Isomorphisms            | 0m01.88s
0m01.74s | theories/categories/NaturalTransformation/Paths                   | 0m01.72s
0m01.65s | theories/categories/NaturalTransformation/Composition/Laws        | 0m01.72s
0m01.64s | theories/categories/FunctorCategory/Morphisms                     | 0m01.66s
0m01.41s | theories/categories/Category/Sigma/OnObjects                      | 0m01.35s
0m01.36s | theories/categories/NaturalTransformation/Composition/Functorial  | 0m01.31s
0m01.36s | theories/categories/NaturalTransformation/Composition/Core        | 0m01.36s
0m01.30s | theories/categories/Category/Prod                                 | 0m01.31s
0m01.28s | theories/categories/NaturalTransformation/Pointwise               | 0m01.32s
0m01.27s | theories/types/Prod                                               | 0m01.31s
0m01.15s | theories/categories/Functor/Pointwise                             | 0m01.14s
0m01.09s | theories/categories/ExponentialLaws/Law  N/A                      | 0m01.00s
0m01.06s | theories/categories/Limits/Core                                   | 0m01.26s
0m01.02s | theories/categories/ExponentialLaws/Law1/Functors                 | 0m01.06s
0m01.00s | theories/categories/NaturalTransformation/Prod                    | 0m00.99s
0m00.99s | theories/hit/Spheres                                              | 0m01.05s
0m00.92s | theories/categories/Functor/Prod                                  | 0m00.91s
0m00.89s | theories/hit/epi                                                  | 0m00.83s
0m00.88s | theories/types/Paths                                              | 0m00.85s
0m00.86s | theories/categories/Functor/Composition/Functorial                | 0m00.79s
0m00.85s | theories/Trunc                                                    | 0m00.81s
0m00.73s | theories/categories/KanExtensions/Core                            | 0m00.69s
0m00.64s | theories/types/Universe                                           | 0m00.68s
0m00.60s | theories/categories/InitialTerminalCategory                       | 0m00.68s
0m00.60s | theories/types/Sum                                                | 0m00.61s
0m00.56s | theories/hit/quotient                                             | 0m00.54s
0m00.55s | theories/Functorish                                               | 0m00.68s
0m00.54s | theories/categories/Comma/Projection                              | 0m00.49s
0m00.53s | theories/categories/categories                                    | 0m00.52s
0m00.53s | theories/categories/NaturalTransformation/Sum                     | 0m00.52s
0m00.53s | theories/types/Record                                             | 0m00.48s
0m00.52s | theories/hit/Suspension                                           | 0m00.63s
0m00.52s | theories/hit/Circle                                               | 0m00.51s
0m00.48s | theories/categories/Functor/Composition/Laws                      | 0m00.50s
0m00.47s | theories/categories/Limits/Functors                               | 0m00.45s
0m00.46s | theories/categories/ExponentialLaws/Law3/Functors                 | 0m00.45s
0m00.44s | theories/types/Forall                                             | 0m00.43s
0m00.44s | theories/HProp                                                    | 0m00.41s
0m00.42s | theories/categories/Cat/Core                                      | 0m00.45s
0m00.42s | theories/Tactics                                                  | 0m00.45s
0m00.40s | theories/categories/KanExtensions/Functors                        | 0m00.44s
0m00.39s | theories/categories/Functor/Functor                               | 0m00.44s
0m00.38s | theories/Fibrations                                               | 0m00.42s
0m00.37s | theories/hit/minus1Trunc                                          | 0m00.28s
0m00.35s | theories/HSet                                                     | 0m00.38s
0m00.34s | theories/TruncType                                                | 0m00.31s
0m00.32s | theories/Misc                                                     | 0m00.28s
0m00.32s | theories/categories/IndiscreteCategory                            | 0m00.33s
0m00.30s | theories/categories/Cat/Morphisms                                 | 0m00.27s
0m00.29s | theories/categories/Functor/Dual                                  | 0m00.32s
0m00.28s | theories/types/Arrow                                              | 0m00.22s
0m00.28s | theories/categories/NaturalTransformation/Identity                | 0m00.26s
0m00.26s | theories/categories/ExponentialLaws/ExponentialLaws               | 0m00.26s
0m00.26s | theories/categories/Functor/Composition/Core                      | 0m00.23s
0m00.23s | theories/categories/Notations                                     | 0m00.22s
0m00.22s | theories/categories/Category/Objects                              | 0m00.24s
0m00.22s | theories/hit/iso                                                  | 0m00.20s
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0m00.21s | theories/Conjugation                                              | 0m00.18s
0m00.21s | theories/categories/Adjoint/Adjoint                               | 0m00.22s
0m00.20s | theories/categories/FunctorCategory/Core                          | 0m00.19s
0m00.20s | theories/categories/NaturalTransformation/NaturalTransformation   | 0m00.17s
0m00.20s | theories/FunextVarieties                                          | 0m00.19s
0m00.18s | theories/categories/Comma/Comma                                   | 0m00.19s
0m00.18s | theories/categories/Functor/Prod/Prod                             | 0m00.15s
0m00.18s | theories/categories/Cat/Cat                                       | 0m00.14s
0m00.17s | theories/categories/SetCategory/Functors/Functors                 | 0m00.19s
0m00.17s | theories/categories/NatCategory                                   | 0m00.22s
0m00.17s | theories/categories/Pseudofunctor/Pseudofunctor                   | 0m00.16s
0m00.16s | theories/categories/Profunctor/Representable                      | 0m00.14s
0m00.16s | theories/categories/FunctorCategory/Utf8                          | 0m00.18s
0m00.16s | theories/Overture                                                 | 0m00.16s
0m00.16s | theories/categories/Adjoint/Utf8                                  | 0m00.16s
0m00.16s | theories/categories/GroupoidCategory/Core                         | 0m00.14s
0m00.16s | theories/hit/unique_choice                                        | 0m00.15s
0m00.16s | theories/categories/ExponentialLaws/Law3/Law3                     | 0m00.18s
0m00.16s | theories/types/Unit                                               | 0m00.11s
0m00.16s | theories/categories/ExponentialLaws/Law1/Law1                     | 0m00.16s
0m00.15s | theories/categories/Limits/Limits                                 | 0m00.18s
0m00.15s | theories/categories/NaturalTransformation/Notations               | 0m00.15s
0m00.15s | contrib/HoTTBook                                                  | 0m00.16s
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0m00.15s | theories/categories/Adjoint/Composition/Composition               | 0m00.15s
0m00.15s | theories/categories/Comma/Notations                               | 0m00.14s
0m00.14s | theories/hit/Interval                                             | 0m00.16s
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0m00.14s | theories/categories/Profunctor/Core                               | 0m00.10s
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0m00.14s | theories/categories/Category/Sigma/Sigma                          | 0m00.16s
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0m00.14s | theories/types/Bool                                               | 0m00.13s
0m00.14s | theories/categories/Adjoint/Notations                             | 0m00.13s
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0m00.14s | theories/categories/Category/Univalent                            | 0m00.14s
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0m00.13s | theories/categories/SetCategory/Core                              | 0m00.14s
0m00.13s | theories/categories/Comma/Utf8                                    | 0m00.13s
0m00.13s | theories/categories/FunctorCategory/FunctorCategory               | 0m00.15s
0m00.13s | theories/categories/Profunctor/Notations                          | 0m00.11s
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0m00.13s | theories/categories/Functor/Notations                             | 0m00.15s
0m00.13s | theories/categories/KanExtensions/KanExtensions                   | 0m00.15s
0m00.12s | theories/categories/Category/Subcategory/Subcategory              | 0m00.12s
0m00.12s | theories/categories/Adjoint/Identity                              | 0m00.13s
0m00.12s | theories/categories/ExponentialLaws/Law4/Law4                     | 0m00.10s
0m00.12s | theories/Contractible                                             | 0m00.13s
0m00.12s | theories/categories/Functor/Core                                  | 0m00.12s
0m00.12s | theories/UnivalenceAxiom                                          | 0m00.10s
0m00.12s | theories/categories/FunctorCategory/Notations                     | 0m00.12s
0m00.12s | theories/categories/Category/Subcategory/Full                     | 0m00.13s
0m00.12s | theories/categories/Functor/Utf8                                  | 0m00.16s
0m00.12s | theories/categories/DiscreteCategory                              | 0m00.10s
0m00.12s | theories/categories/Category/Core                                 | 0m00.14s
0m00.12s | theories/categories/NaturalTransformation/Composition/Composition | 0m00.11s
0m00.12s | theories/categories/ExponentialLaws/Law2/Law2                     | 0m00.13s
0m00.12s | theories/HoTT                                                     | 0m00.11s
0m00.11s | theories/categories/Category/Utf8                                 | 0m00.14s
0m00.11s | theories/categories/Category/Subcategory/Wide                     | 0m00.12s
0m00.10s | theories/categories/SetCategory/SetCategory                       | 0m00.09s
0m00.10s | coq/theories/Init/Peano                                           | 0m00.10s
0m00.10s | theories/categories/GroupoidCategory/GroupoidCategory             | 0m00.14s
0m00.08s | theories/categories/Adjoint/Core                                  | 0m00.14s
0m00.08s | theories/categories/Profunctor/Utf8                               | 0m00.12s
0m00.08s | theories/types/Empty                                              | 0m00.07s
0m00.07s | coq/theories/Init/Logic_Type                                      | 0m00.06s
0m00.07s | theories/categories/Functor/Identity                              | 0m00.07s
0m00.07s | theories/Pointed                                                  | 0m00.08s
0m00.06s | theories/FunextAxiom                                              | 0m00.05s
0m00.06s | coq/theories/Program/Tactics                                      | 0m00.04s
0m00.06s | coq/theories/Init/Specif                                          | 0m00.09s
0m00.05s | coq/theories/Init/Datatypes                                       | 0m00.06s
0m00.05s | theories/categories/Category/Strict                               | 0m00.07s
0m00.04s | coq/theories/Init/Notations                                       | 0m00.03s
0m00.04s | coq/theories/Init/Prelude                                         | 0m00.03s
0m00.03s | coq/theories/Init/Logic                                           | 0m00.04s
0m00.02s | coq/theories/Init/Tactics                                         | 0m00.02s
0m00.02s | coq/theories/Bool/Bool                                            | 0m00.03s
Add a helper lemma for associativity on 4 things
Add the grothendieck construction

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8m35.11s | Total                                                             | 8m11.41s
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1m53.15s | theories/categories/Comma/ProjectionFunctors                      | 2m00.61s
0m32.72s | theories/categories/Adjoint/Composition/AssociativityLaw          | 0m33.59s
0m31.70s | theories/categories/Comma/Dual                                    | 0m28.36s
0m26.06s | theories/categories/Grothendieck/PseudofunctorToCat               |   N/A
0m17.52s | theories/categories/ExponentialLaws/Law4/Functors                 | 0m17.78s
0m16.25s | theories/categories/Adjoint/UnitCounitCoercions                   | 0m17.43s
0m16.22s | theories/categories/Comma/InducedFunctors                         | 0m16.10s
0m13.37s | theories/categories/Adjoint/Composition/Core                      | 0m12.46s
0m13.36s | theories/hit/Flattening                                           | 0m13.31s
0m12.36s | theories/categories/Pseudofunctor/Core                            | 0m12.50s
0m12.35s | theories/categories/Adjoint/Dual                                  | 0m12.04s
0m10.91s | theories/categories/Pseudofunctor/FromFunctor                     | 0m11.06s
0m10.66s | theories/categories/Adjoint/Composition/IdentityLaws              | 0m10.13s
0m09.73s | theories/categories/Functor/Pointwise/Properties                  | 0m10.12s
0m08.26s | theories/categories/Functor/Prod/Universal                        | 0m08.80s
0m08.25s | theories/categories/GroupoidCategory/Morphisms                    | 0m08.26s
0m08.14s | theories/categories/ExponentialLaws/Law1/Law                      | 0m08.31s
0m07.46s | theories/hit/Connectedness                                        | 0m07.78s
0m06.80s | theories/categories/Adjoint/Paths                                 | 0m06.57s
0m06.76s | theories/categories/UniversalProperties                           | 0m06.99s
0m05.92s | theories/categories/Functor/Sum                                   | 0m05.68s
0m05.78s | theories/categories/Category/Morphisms                            | 0m05.93s
0m05.76s | theories/categories/Functor/Paths                                 | 0m05.76s
0m05.55s | theories/categories/Adjoint/UnitCounit                            | 0m05.70s
0m05.20s | theories/categories/DualFunctor                                   | 0m05.46s
0m05.11s | theories/categories/ExponentialLaws/Law2/Functors                 | 0m05.01s
0m05.06s | theories/EquivalenceVarieties                                     | 0m04.99s
0m04.29s | theories/categories/Category/Sigma/OnMorphisms                    | 0m04.18s
0m03.59s | theories/categories/ProductLaws                                   | 0m03.78s
0m03.55s | theories/types/ObjectClassifier                                   | 0m03.77s
0m03.15s | theories/types/Sigma                                              | 0m03.10s
0m02.82s | theories/categories/Grothendieck/ToSet                            |   N/A
0m02.79s | theories/categories/Functor/Prod/Functorial                       | 0m02.67s
0m02.77s | theories/categories/Adjoint/UniversalMorphisms                    | 0m02.82s
0m02.69s | theories/categories/FunctorCategory/Functorial                    | 0m02.72s
0m02.66s | theories/Equivalences                                             | 0m02.57s
0m02.31s | theories/categories/Functor/Attributes                            | 0m02.19s
0m02.31s | theories/categories/Category/Sum                                  | 0m02.28s
0m02.14s | theories/categories/Category/Sigma/Core                           | 0m02.12s
0m02.08s | theories/categories/Comma/Core                                    | 0m02.03s
0m01.94s | theories/PathGroupoids                                            | 0m01.97s
0m01.89s | theories/categories/NaturalTransformation/Dual                    | 0m01.86s
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0m01.72s | theories/categories/NaturalTransformation/Composition/Laws        | 0m01.65s
0m01.62s | theories/categories/NaturalTransformation/Paths                   | 0m01.67s
0m01.61s | theories/categories/FunctorCategory/Morphisms                     | 0m01.64s
0m01.38s | theories/categories/Category/Sigma/OnObjects                      | 0m01.36s
0m01.35s | theories/categories/NaturalTransformation/Composition/Core        | 0m01.37s
0m01.35s | theories/categories/Category/Prod                                 | 0m01.31s
0m01.31s | theories/types/Prod                                               | 0m01.28s
0m01.22s | theories/categories/NaturalTransformation/Composition/Functorial  | 0m01.31s
0m01.22s | theories/categories/Limits/Core                                   | 0m01.07s
0m01.22s | theories/categories/NaturalTransformation/Pointwise               | 0m01.26s
0m01.06s | theories/categories/Functor/Pointwise                             | 0m01.04s
0m01.02s | theories/hit/Spheres                                              | 0m01.06s
0m00.99s | theories/categories/ExponentialLaws/Law  N/A                      | 0m01.00s
0m00.99s | theories/categories/NaturalTransformation/Prod                    | 0m00.97s
0m00.98s | theories/categories/ExponentialLaws/Law1/Functors                 | 0m01.02s
0m00.89s | theories/categories/Functor/Prod                                  | 0m00.87s
0m00.89s | theories/hit/epi                                                  | 0m00.86s
0m00.87s | theories/categories/Functor/Composition/Functorial                | 0m00.86s
0m00.86s | theories/Trunc                                                    | 0m00.80s
0m00.81s | theories/types/Paths                                              | 0m00.86s
0m00.71s | theories/categories/KanExtensions/Core                            | 0m00.68s
0m00.67s | theories/types/Sum                                                | 0m00.59s
0m00.63s | theories/categories/InitialTerminalCategory                       | 0m00.64s
0m00.60s | theories/types/Universe                                           | 0m00.64s
0m00.58s | theories/categories/categories                                    | 0m00.50s
0m00.55s | theories/hit/quotient                                             | 0m00.55s
0m00.55s | theories/categories/NaturalTransformation/Sum                     | 0m00.57s
0m00.55s | theories/types/Record                                             | 0m00.52s
0m00.54s | theories/categories/Comma/Projection                              | 0m00.56s
0m00.53s | theories/Functorish                                               | 0m00.65s
0m00.52s | theories/categories/Functor/Composition/Laws                      | 0m00.50s
0m00.49s | theories/hit/Suspension                                           | 0m00.54s
0m00.49s | theories/types/Forall                                             | 0m00.43s
0m00.49s | theories/categories/ExponentialLaws/Law3/Functors                 | 0m00.42s
0m00.48s | theories/hit/Circle                                               | 0m00.46s
0m00.46s | theories/HProp                                                    | 0m00.44s
0m00.42s | theories/categories/KanExtensions/Functors                        | 0m00.45s
0m00.42s | theories/categories/Functor/Functor                               | 0m00.41s
0m00.40s | theories/categories/Limits/Functors                               | 0m00.48s
0m00.38s | theories/categories/Cat/Core                                      | 0m00.33s
0m00.38s | theories/HSet                                                     | 0m00.37s
0m00.37s | theories/Tactics                                                  | 0m00.42s
0m00.36s | theories/Fibrations                                               | 0m00.38s
0m00.36s | theories/TruncType                                                | 0m00.34s
0m00.35s | theories/categories/ExponentialLaws/ExponentialLaws               | 0m00.27s
0m00.34s | theories/categories/Cat/Morphisms                                 | 0m00.28s
0m00.34s | theories/categories/Functor/Dual                                  | 0m00.30s
0m00.32s | theories/hit/minus1Trunc                                          | 0m00.27s
0m00.32s | theories/categories/NaturalTransformation/Identity                | 0m00.29s
0m00.30s | theories/Misc                                                     | 0m00.26s
0m00.29s | theories/categories/IndiscreteCategory                            | 0m00.28s
0m00.26s | theories/categories/Grothendieck/Grothendieck                     |   N/A
0m00.26s | theories/categories/Functor/Composition/Core                      | 0m00.22s
0m00.26s | theories/categories/Category/Objects                              | 0m00.26s
0m00.24s | theories/categories/Adjoint/Adjoint                               | 0m00.22s
0m00.23s | theories/categories/NaturalTransformation/Utf8                    | 0m00.16s
0m00.23s | theories/categories/SetCategory/Functors/Functors                 | 0m00.18s
0m00.23s | theories/types/Arrow                                              | 0m00.26s
0m00.23s | theories/categories/Utf8                                          | 0m00.22s
0m00.21s | theories/categories/Notations                                     | 0m00.22s
0m00.21s | theories/categories/Grothendieck/ToCat                            |   N/A
0m00.21s | theories/categories/NatCategory                                   | 0m00.19s
0m00.20s | theories/Conjugation                                              | 0m00.16s
0m00.20s | theories/FunextVarieties                                          | 0m00.16s
0m00.19s | theories/categories/Comma/Comma                                   | 0m00.21s
0m00.19s | theories/categories/FunctorCategory/Core                          | 0m00.19s
0m00.19s | theories/hit/iso                                                  | 0m00.18s
0m00.18s | theories/hit/unique_choice                                        | 0m00.16s
0m00.18s | theories/categories/ExponentialLaws/Law3/Law3                     | 0m00.14s
0m00.18s | theories/categories/Cat/Cat                                       | 0m00.17s
0m00.17s | theories/categories/Limits/Limits                                 | 0m00.18s
0m00.17s | theories/categories/Adjoint/Composition/LawsTactic                | 0m00.15s
0m00.17s | theories/categories/NaturalTransformation/Core                    | 0m00.14s
0m00.17s | theories/categories/Functor/Prod/Prod                             | 0m00.15s
0m00.17s | theories/categories/KanExtensions/KanExtensions                   | 0m00.17s
0m00.17s | theories/categories/Category/Dual                                 | 0m00.14s
0m00.17s | theories/categories/NaturalTransformation/NaturalTransformation   | 0m00.24s
0m00.17s | theories/categories/Pseudofunctor/Pseudofunctor                   | 0m00.18s
0m00.17s | theories/categories/Category/Core                                 | 0m00.16s
0m00.16s | theories/categories/Profunctor/Representable                      | 0m00.14s
0m00.16s | theories/Overture                                                 | 0m00.11s
0m00.16s | theories/categories/Adjoint/Composition/Composition               | 0m00.18s
0m00.16s | theories/categories/Adjoint/Notations                             | 0m00.17s
0m00.16s | theories/categories/Category/Univalent                            | 0m00.14s
0m00.15s | theories/categories/Adjoint/Identity                              | 0m00.13s
0m00.15s | theories/categories/Adjoint/Utf8                                  | 0m00.17s
0m00.15s | theories/categories/Category/Category                             | 0m00.12s
0m00.15s | theories/categories/GroupoidCategory/Core                         | 0m00.16s
0m00.15s | theories/categories/ExponentialLaws/Law2/Law2                     | 0m00.15s
0m00.14s | theories/categories/Profunctor/Core                               | 0m00.12s
0m00.14s | theories/categories/NaturalTransformation/Notations               | 0m00.16s
0m00.14s | theories/categories/FunctorCategory/FunctorCategory               | 0m00.19s
0m00.14s | theories/categories/Category/Subcategory/Wide                     | 0m00.14s
0m00.14s | theories/categories/Functor/Notations                             | 0m00.16s
0m00.14s | theories/categories/NaturalTransformation/Composition/Composition | 0m00.12s
0m00.14s | theories/HoTT                                                     | 0m00.11s
0m00.13s | theories/hit/Interval                                             | 0m00.12s
0m00.13s | theories/categories/FunctorCategory/Utf8                          | 0m00.13s
0m00.13s | theories/categories/Profunctor/Identity                           | 0m00.12s
0m00.13s | theories/categories/Profunctor/Profunctor                         | 0m00.12s
0m00.13s | contrib/HoTTBook                                                  | 0m00.12s
0m00.13s | theories/categories/Functor/Composition/Composition               | 0m00.11s
0m00.13s | theories/categories/Category/Subcategory/Full                     | 0m00.10s
0m00.13s | theories/types/Unit                                               | 0m00.15s
0m00.13s | theories/categories/Functor/Utf8                                  | 0m00.13s
0m00.13s | theories/categories/ExponentialLaws/Law1/Law1                     | 0m00.16s
0m00.12s | theories/categories/Functor/Pointwise/Pointwise                   | 0m00.11s
0m00.12s | theories/categories/SetCategory/Core                              | 0m00.12s
0m00.12s | theories/categories/Comma/Utf8                                    | 0m00.16s
0m00.12s | theories/categories/Profunctor/Notations                          | 0m00.10s
0m00.12s | theories/types/Bool                                               | 0m00.11s
0m00.12s | theories/hit/Truncations                                          | 0m00.13s
0m00.12s | theories/categories/Profunctor/Utf8                               | 0m00.14s
0m00.12s | theories/categories/Comma/Notations                               | 0m00.14s
0m00.12s | theories/categories/DiscreteCategory                              | 0m00.11s
0m00.11s | theories/Contractible                                             | 0m00.11s
0m00.11s | theories/categories/Category/Notations                            | 0m00.12s
0m00.11s | theories/categories/FunctorCategory/Notations                     | 0m00.12s
0m00.10s | theories/categories/SetCategory/SetCategory                       | 0m00.12s
0m00.10s | theories/categories/Category/Sigma/Sigma                          | 0m00.13s
0m00.10s | theories/categories/Functor/Core                                  | 0m00.10s
0m00.09s | theories/categories/Category/Subcategory/Subcategory              | 0m00.11s
0m00.09s | theories/categories/Category/Utf8                                 | 0m00.11s
0m00.09s | coq/theories/Init/Peano                                           | 0m00.10s
0m00.09s | theories/categories/GroupoidCategory/GroupoidCategory             | 0m00.10s
0m00.08s | theories/FunextAxiom                                              | 0m00.07s
0m00.08s | theories/categories/ExponentialLaws/Law4/Law4                     | 0m00.09s
0m00.08s | theories/categories/Adjoint/Core                                  | 0m00.13s
0m00.08s | theories/UnivalenceAxiom                                          | 0m00.11s
0m00.08s | theories/categories/Category/Strict                               | 0m00.08s
0m00.08s | theories/Pointed                                                  | 0m00.10s
0m00.08s | coq/theories/Init/Specif                                          | 0m00.07s
0m00.07s | theories/types/Empty                                              | 0m00.08s
0m00.06s | coq/theories/Init/Datatypes                                       | 0m00.05s
0m00.06s | coq/theories/Init/Logic_Type                                      | 0m00.08s
0m00.06s | theories/categories/Functor/Identity                              | 0m00.08s
0m00.05s | coq/theories/Init/Notations                                       | 0m00.04s
0m00.05s | coq/theories/Program/Tactics                                      | 0m00.06s
0m00.04s | coq/theories/Init/Logic                                           | 0m00.04s
0m00.04s | coq/theories/Init/Prelude                                         | 0m00.04s
0m00.03s | coq/theories/Init/Tactics                                         | 0m00.02s
0m00.03s | coq/theories/Bool/Bool                                            | 0m00.04s
Define the category of sections

After    | File Name                                                         | Before
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8m41.62s | Total                                                             | 8m43.79s
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2m00.25s | theories/categories/Comma/ProjectionFunctors                      | 2m01.08s
0m32.81s | theories/categories/Adjoint/Composition/AssociativityLaw          | 0m33.00s
0m30.10s | theories/categories/Comma/Dual                                    | 0m28.94s
0m24.90s | theories/categories/Grothendieck/PseudofunctorToCat               | 0m24.99s
0m17.08s | theories/categories/ExponentialLaws/Law4/Functors                 | 0m17.94s
0m17.04s | theories/categories/Comma/InducedFunctors                         | 0m16.24s
0m16.93s | theories/categories/Adjoint/UnitCounitCoercions                   | 0m16.68s
0m12.83s | theories/categories/Adjoint/Composition/Core                      | 0m13.32s
0m12.74s | theories/hit/Flattening                                           | 0m13.16s
0m12.62s | theories/categories/Adjoint/Dual                                  | 0m13.36s
0m12.45s | theories/categories/Pseudofunctor/Core                            | 0m12.56s
0m11.07s | theories/categories/Adjoint/Composition/IdentityLaws              | 0m11.02s
0m10.93s | theories/categories/Pseudofunctor/FromFunctor                     | 0m11.92s
0m10.04s | theories/categories/Functor/Pointwise/Properties                  | 0m09.58s
0m08.28s | theories/categories/Functor/Prod/Universal                        | 0m08.15s
0m08.21s | theories/categories/ExponentialLaws/Law1/Law                      | 0m08.35s
0m07.98s | theories/categories/GroupoidCategory/Morphisms                    | 0m08.00s
0m07.57s | theories/hit/Connectedness                                        | 0m07.32s
0m07.14s | theories/categories/Adjoint/Paths                                 | 0m06.44s
0m06.82s | theories/categories/UniversalProperties                           | 0m06.97s
0m05.82s | theories/categories/Functor/Paths                                 | 0m05.76s
0m05.82s | theories/categories/Functor/Sum                                   | 0m05.70s
0m05.69s | theories/categories/Category/Morphisms                            | 0m06.13s
0m05.50s | theories/categories/Adjoint/UnitCounit                            | 0m05.99s
0m05.48s | theories/categories/DualFunctor                                   | 0m05.66s
0m05.26s | theories/EquivalenceVarieties                                     | 0m05.42s
0m04.84s | theories/categories/ExponentialLaws/Law2/Functors                 | 0m05.20s
0m04.07s | theories/categories/Category/Sigma/OnMorphisms                    | 0m04.10s
0m03.73s | theories/types/ObjectClassifier                                   | 0m03.51s
0m03.61s | theories/categories/ProductLaws                                   | 0m04.02s
0m03.09s | theories/types/Sigma                                              | 0m03.00s
0m02.79s | theories/categories/FunctorCategory/Functorial                    | 0m02.65s
0m02.77s | theories/categories/Functor/Prod/Functorial                       | 0m02.77s
0m02.75s | theories/categories/Adjoint/UniversalMorphisms                    | 0m02.70s
0m02.54s | theories/Equivalences                                             | 0m02.57s
0m02.51s | theories/categories/Grothendieck/ToSet                            | 0m02.78s
0m02.24s | theories/categories/Functor/Attributes                            | 0m02.30s
0m02.16s | theories/categories/Comma/Core                                    | 0m02.21s
0m02.15s | theories/categories/Category/Sum                                  | 0m02.24s
0m02.06s | theories/categories/Category/Sigma/Core                           | 0m02.01s
0m01.94s | theories/categories/NaturalTransformation/Isomorphisms            | 0m01.86s
0m01.87s | theories/PathGroupoids                                            | 0m01.82s
0m01.86s | theories/categories/NaturalTransformation/Dual                    | 0m01.86s
0m01.82s | theories/categories/HomFunctor                                    | 0m01.70s
0m01.70s | theories/categories/NaturalTransformation/Composition/Laws        | 0m01.71s
0m01.70s | theories/categories/NaturalTransformation/Paths                   | 0m01.67s
0m01.60s | theories/categories/FunctorCategory/Morphisms                     | 0m01.91s
0m01.50s | theories/categories/Category/Sigma/OnObjects                      | 0m01.46s
0m01.31s | theories/categories/NaturalTransformation/Composition/Core        | 0m01.39s
0m01.28s | theories/types/Prod                                               | 0m01.34s
0m01.28s | theories/categories/Category/Prod                                 | 0m01.32s
0m01.24s | theories/categories/NaturalTransformation/Composition/Functorial  | 0m01.24s
0m01.23s | theories/categories/NaturalTransformation/Pointwise               | 0m01.30s
0m01.21s | theories/categories/Limits/Core                                   | 0m01.10s
0m01.12s | theories/categories/Functor/Pointwise                             | 0m01.07s
0m01.10s | theories/hit/Spheres                                              | 0m00.93s
0m01.07s | theories/categories/CategoryOfSections/Core                       |   N/A
0m01.06s | theories/categories/ExponentialLaws/Law  N/A                      | 0m01.23s
0m01.00s | theories/categories/ExponentialLaws/Law1/Functors                 | 0m01.05s
0m00.95s | theories/categories/NaturalTransformation/Prod                    | 0m01.13s
0m00.93s | theories/categories/Functor/Prod                                  | 0m00.94s
0m00.92s | theories/hit/epi                                                  | 0m00.92s
0m00.85s | theories/categories/Functor/Composition/Functorial                | 0m00.83s
0m00.83s | theories/types/Paths                                              | 0m00.79s
0m00.81s | theories/Trunc                                                    | 0m00.84s
0m00.76s | theories/categories/KanExtensions/Core                            | 0m00.71s
0m00.66s | theories/types/Universe                                           | 0m00.61s
0m00.64s | theories/categories/InitialTerminalCategory                       | 0m00.64s
0m00.59s | theories/types/Sum                                                | 0m00.60s
0m00.58s | theories/Functorish                                               | 0m00.56s
0m00.57s | theories/types/Record                                             | 0m00.49s
0m00.56s | theories/categories/Comma/Projection                              | 0m00.52s
0m00.56s | theories/categories/NaturalTransformation/Sum                     | 0m00.56s
0m00.55s | theories/hit/quotient                                             | 0m00.55s
0m00.53s | theories/hit/Suspension                                           | 0m00.52s
0m00.52s | theories/categories/Functor/Composition/Laws                      | 0m00.50s
0m00.49s | theories/categories/categories                                    | 0m00.52s
0m00.49s | theories/hit/Circle                                               | 0m00.48s
0m00.47s | theories/categories/Limits/Functors                               | 0m00.47s
0m00.46s | theories/categories/KanExtensions/Functors                        | 0m00.49s
0m00.44s | theories/categories/Functor/Functor                               | 0m00.36s
0m00.44s | theories/Tactics                                                  | 0m00.42s
0m00.42s | theories/types/Forall                                             | 0m00.45s
0m00.42s | theories/HProp                                                    | 0m00.44s
0m00.42s | theories/categories/ExponentialLaws/Law3/Functors                 | 0m00.43s
0m00.41s | theories/categories/Cat/Core                                      | 0m00.40s
0m00.38s | theories/categories/ExponentialLaws/ExponentialLaws               | 0m00.28s
0m00.38s | theories/Fibrations                                               | 0m00.35s
0m00.38s | theories/HSet                                                     | 0m00.37s
0m00.34s | theories/hit/minus1Trunc                                          | 0m00.27s
0m00.32s | theories/TruncType                                                | 0m00.30s
0m00.30s | theories/categories/Functor/Dual                                  | 0m00.32s
0m00.30s | theories/categories/IndiscreteCategory                            | 0m00.33s
0m00.30s | theories/categories/NaturalTransformation/Identity                | 0m00.27s
0m00.28s | theories/Misc                                                     | 0m00.30s
0m00.28s | theories/categories/Cat/Morphisms                                 | 0m00.32s
0m00.26s | theories/categories/Grothendieck/Grothendieck                     | 0m00.26s
0m00.26s | theories/categories/Grothendieck/ToCat                            | 0m00.18s
0m00.26s | theories/types/Arrow                                              | 0m00.27s
0m00.25s | theories/categories/Category/Objects                              | 0m00.24s
0m00.22s | theories/categories/FunctorCategory/Core                          | 0m00.15s
0m00.21s | theories/categories/SetCategory/Functors/Functors                 | 0m00.21s
0m00.20s | theories/Conjugation                                              | 0m00.22s
0m00.20s | theories/categories/Adjoint/Adjoint                               | 0m00.24s
0m00.20s | theories/categories/Functor/Composition/Core                      | 0m00.24s
0m00.20s | theories/categories/ExponentialLaws/Law2/Law2                     | 0m00.17s
0m00.19s | theories/categories/Notations                                     | 0m00.22s
0m00.19s | theories/categories/Adjoint/Utf8                                  | 0m00.14s
0m00.19s | theories/categories/GroupoidCategory/Core                         | 0m00.19s
0m00.19s | theories/categories/Profunctor/Utf8                               | 0m00.14s
0m00.18s | theories/categories/NaturalTransformation/Utf8                    | 0m00.17s
0m00.18s | theories/categories/Comma/Comma                                   | 0m00.16s
0m00.18s | theories/categories/NatCategory                                   | 0m00.16s
0m00.18s | theories/hit/iso                                                  | 0m00.20s
0m00.17s | theories/categories/Profunctor/Representable                      | 0m00.13s
0m00.17s | theories/categories/Adjoint/Composition/LawsTactic                | 0m00.13s
0m00.17s | theories/categories/Category/Category                             | 0m00.13s
0m00.17s | theories/categories/Utf8                                          | 0m00.26s
0m00.16s | theories/categories/Limits/Limits                                 | 0m00.14s
0m00.16s | theories/categories/FunctorCategory/Utf8                          | 0m00.17s
0m00.16s | theories/categories/NaturalTransformation/Core                    | 0m00.14s
0m00.16s | theories/categories/Functor/Composition/Composition               | 0m00.17s
0m00.16s | theories/categories/Adjoint/Composition/Composition               | 0m00.18s
0m00.16s | theories/categories/Category/Dual                                 | 0m00.17s
0m00.16s | theories/categories/ExponentialLaws/Law3/Law3                     | 0m00.14s
0m00.16s | theories/categories/NaturalTransformation/NaturalTransformation   | 0m00.20s
0m00.16s | theories/categories/Pseudofunctor/Pseudofunctor                   | 0m00.17s
0m00.16s | theories/FunextVarieties                                          | 0m00.15s
0m00.16s | theories/categories/Category/Core                                 | 0m00.14s
0m00.15s | theories/Overture                                                 | 0m00.14s
0m00.15s | theories/categories/Comma/Utf8                                    | 0m00.17s
0m00.15s | theories/categories/NaturalTransformation/Notations               | 0m00.14s
0m00.15s | theories/categories/FunctorCategory/FunctorCategory               | 0m00.22s
0m00.15s | theories/categories/Functor/Prod/Prod                             | 0m00.19s
0m00.15s | theories/categories/Functor/Notations                             | 0m00.16s
0m00.15s | theories/hit/unique_choice                                        | 0m00.16s
0m00.15s | theories/HoTT                                                     | 0m00.13s
0m00.14s | theories/categories/Profunctor/Profunctor                         | 0m00.12s
0m00.14s | theories/categories/SetCategory/Core                              | 0m00.16s
0m00.14s | theories/categories/Adjoint/Identity                              | 0m00.15s
0m00.14s | theories/categories/Profunctor/Notations                          | 0m00.13s
0m00.14s | theories/categories/Adjoint/Core                                  | 0m00.14s
0m00.14s | theories/categories/KanExtensions/KanExtensions                   | 0m00.16s
0m00.14s | theories/categories/Adjoint/Notations                             | 0m00.15s
0m00.14s | theories/categories/FunctorCategory/Notations                     | 0m00.11s
0m00.14s | theories/categories/Comma/Notations                               | 0m00.13s
0m00.14s | theories/categories/Functor/Utf8                                  | 0m00.18s
0m00.14s | theories/categories/NaturalTransformation/Composition/Composition | 0m00.10s
0m00.13s | theories/categories/Category/Utf8                                 | 0m00.10s
0m00.13s | contrib/HoTTBook                                                  | 0m00.14s
0m00.13s | theories/categories/Category/Notations                            | 0m00.14s
0m00.13s | theories/categories/ExponentialLaws/Law1/Law1                     | 0m00.19s
0m00.12s | theories/categories/Profunctor/Identity                           | 0m00.14s
0m00.12s | theories/categories/Functor/Core                                  | 0m00.11s
0m00.12s | theories/UnivalenceAxiom                                          | 0m00.09s
0m00.12s | theories/types/Bool                                               | 0m00.14s
0m00.12s | theories/categories/Cat/Cat                                       | 0m00.13s
0m00.12s | theories/types/Unit                                               | 0m00.14s
0m00.12s | theories/categories/DiscreteCategory                              | 0m00.09s
0m00.11s | theories/hit/Interval                                             | 0m00.16s
0m00.11s | theories/categories/ExponentialLaws/Law4/Law4                     | 0m00.13s
0m00.11s | theories/Contractible                                             | 0m00.09s
0m00.11s | theories/categories/GroupoidCategory/GroupoidCategory             | 0m00.10s
0m00.10s | theories/categories/Profunctor/Core                               | 0m00.16s
0m00.10s | theories/categories/Category/Subcategory/Wide                     | 0m00.11s
0m00.10s | theories/categories/SetCategory/SetCategory                       | 0m00.10s
0m00.10s | coq/theories/Init/Peano                                           | 0m00.08s
0m00.10s | theories/categories/Category/Sigma/Sigma                          | 0m00.16s
0m00.10s | theories/hit/Truncations                                          | 0m00.12s
0m00.10s | theories/categories/Category/Univalent                            | 0m00.12s
0m00.09s | theories/categories/Category/Subcategory/Subcategory              | 0m00.13s
0m00.09s | theories/categories/Functor/Pointwise/Pointwise                   | 0m00.17s
0m00.09s | theories/Pointed                                                  | 0m00.10s
0m00.09s | theories/categories/CategoryOfSections/CategoryOfSections         |   N/A
0m00.08s | theories/FunextAxiom                                              | 0m00.07s
0m00.08s | theories/categories/Category/Strict                               | 0m00.08s
0m00.08s | theories/categories/Category/Subcategory/Full                     | 0m00.12s
0m00.07s | theories/categories/Functor/Identity                              | 0m00.06s
0m00.07s | theories/types/Empty                                              | 0m00.08s
0m00.06s | coq/theories/Init/Datatypes                                       | 0m00.06s
0m00.06s | coq/theories/Init/Specif                                          | 0m00.08s
0m00.05s | coq/theories/Init/Logic_Type                                      | 0m00.08s
0m00.04s | coq/theories/Bool/Bool                                            | 0m00.04s
0m00.04s | coq/theories/Program/Tactics                                      | 0m00.06s
0m00.04s | coq/theories/Init/Prelude                                         | 0m00.03s
0m00.03s | coq/theories/Init/Notations                                       | 0m00.03s
0m00.03s | coq/theories/Init/Tactics                                         | 0m00.03s
0m00.02s | coq/theories/Init/Logic                                           | 0m00.04s
Port dependent product category
Speed up comma/dual by a factor of 5

By explicitly giving proofs and by using Comma.path_morphism.

After    | File Name                                                         | Before
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8m09.36s | Total                                                             | 8m36.43s
---------------------------------------------------------------------------------------
1m53.95s | theories/categories/Comma/ProjectionFunctors                      | 1m54.50s
0m33.47s | theories/categories/Adjoint/Composition/AssociativityLaw          | 0m32.98s
0m24.55s | theories/categories/Grothendieck/PseudofunctorToCat               | 0m24.88s
0m17.53s | theories/categories/ExponentialLaws/Law4/Functors                 | 0m17.24s
0m16.93s | theories/categories/Adjoint/UnitCounitCoercions                   | 0m17.03s
0m16.03s | theories/categories/Comma/InducedFunctors                         | 0m16.00s
0m13.12s | theories/hit/Flattening                                           | 0m13.58s
0m12.58s | theories/categories/Pseudofunctor/Core                            | 0m12.44s
0m12.41s | theories/categories/Adjoint/Composition/Core                      | 0m13.02s
0m12.13s | theories/categories/Adjoint/Dual                                  | 0m12.53s
0m11.22s | theories/categories/Adjoint/Composition/IdentityLaws              | 0m10.26s
0m11.11s | theories/categories/Pseudofunctor/FromFunctor                     | 0m10.86s
0m09.63s | theories/categories/Functor/Pointwise/Properties                  | 0m09.95s
0m08.03s | theories/categories/Functor/Prod/Universal                        | 0m08.40s
0m07.97s | theories/categories/GroupoidCategory/Morphisms                    | 0m07.90s
0m07.90s | theories/categories/ExponentialLaws/Law1/Law                      | 0m07.96s
0m07.38s | theories/hit/Connectedness                                        | 0m07.59s
0m06.74s | theories/categories/Adjoint/Paths                                 | 0m07.28s
0m06.68s | theories/categories/UniversalProperties                           | 0m06.96s
0m05.97s | theories/categories/Comma/Dual                                    | 0m29.94s
0m05.92s | theories/categories/Functor/Sum                                   | 0m05.71s
0m05.78s | theories/categories/Functor/Paths                                 | 0m05.60s
0m05.72s | theories/categories/Category/Morphisms                            | 0m06.22s
0m05.40s | theories/categories/Adjoint/UnitCounit                            | 0m05.40s
0m05.32s | theories/categories/DualFunctor                                   | 0m05.27s
0m05.08s | theories/EquivalenceVarieties                                     | 0m05.47s
0m04.95s | theories/categories/ExponentialLaws/Law2/Functors                 | 0m05.06s
0m04.11s | theories/categories/Category/Sigma/OnMorphisms                    | 0m04.18s
0m03.98s | theories/categories/ProductLaws                                   | 0m03.76s
0m03.82s | theories/types/ObjectClassifier                                   | 0m03.54s
0m03.22s | theories/types/Sigma                                              | 0m03.02s
0m02.76s | theories/categories/Functor/Prod/Functorial                       | 0m02.72s
0m02.74s | theories/categories/Adjoint/UniversalMorphisms                    | 0m02.71s
0m02.65s | theories/categories/FunctorCategory/Functorial                    | 0m02.73s
0m02.60s | theories/Equivalences                                             | 0m02.58s
0m02.59s | theories/categories/Grothendieck/ToSet                            | 0m02.56s
0m02.28s | theories/categories/Functor/Attributes                            | 0m02.46s
0m02.27s | theories/categories/Category/Sum                                  | 0m02.22s
0m02.15s | theories/categories/Comma/Core                                    | 0m02.10s
0m02.13s | theories/categories/Category/Sigma/Core                           | 0m01.98s
0m01.89s | theories/PathGroupoids                                            | 0m01.86s
0m01.81s | theories/categories/NaturalTransformation/Isomorphisms            | 0m01.98s
0m01.80s | theories/categories/HomFunctor                                    | 0m01.74s
0m01.80s | theories/categories/NaturalTransformation/Dual                    | 0m01.96s
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