Formalize the "notion of a structure"

Hopefully we'll soon be moving to polyproj, where I hope we won't have
to deal with this nonsense of defining simple record types for speed of
[destruct].

After    | File Name                                                | Before
------------------------------------------------------------------------------
8m19.20s | Total                                                    | 8m18.55s
------------------------------------------------------------------------------
1m48.24s | categories/Comma/ProjectionFunctors                      | 1m43.91s
0m32.12s | categories/Adjoint/Composition/AssociativityLaw          | 0m32.49s
0m24.18s | categories/Grothendieck/PseudofunctorToCat               | 0m25.28s
0m17.34s | categories/ExponentialLaws/Law4/Functors                 | 0m16.95s
0m16.57s | categories/Adjoint/UnitCounitCoercions                   | 0m16.17s
0m15.38s | categories/Comma/InducedFunctors                         | 0m15.76s
0m14.50s | categories/FunctorCategory/Dual                          | 0m15.56s
0m12.55s | categories/Pseudofunctor/Core                            | 0m12.12s
0m12.45s | categories/Functor/Pointwise/Properties                  | 0m13.25s
0m12.32s | hit/Flattening                                           | 0m12.52s
0m12.10s | categories/Adjoint/Composition/Core                      | 0m12.30s
0m11.14s | categories/Adjoint/Dual                                  | 0m11.55s
0m10.64s | categories/Adjoint/Composition/IdentityLaws              | 0m10.45s
0m10.29s | categories/Pseudofunctor/FromFunctor                     | 0m10.94s
0m07.82s | categories/Yoneda                                        | 0m08.36s
0m07.68s | categories/ExponentialLaws/Law1/Law                      | 0m08.13s
0m07.65s | categories/Functor/Prod/Universal                        | 0m07.67s
0m07.57s | categories/GroupoidCategory/Morphisms                    | 0m07.62s
0m06.72s | hit/Connectedness                                        | 0m06.72s
0m06.59s | categories/UniversalProperties                           | 0m07.19s
0m06.23s | categories/Adjoint/Paths                                 | 0m06.94s
0m06.21s | categories/Comma/Dual                                    | 0m06.19s
0m06.21s | categories/Functor/Paths                                 | 0m05.72s
0m05.98s | categories/Category/Morphisms                            | 0m05.68s
0m05.63s | categories/Functor/Sum                                   | 0m05.62s
0m05.53s | categories/Adjoint/UnitCounit                            | 0m05.92s
0m05.28s | EquivalenceVarieties                                     | 0m05.00s
0m05.26s | categories/ExponentialLaws/Law2/Functors                 | 0m05.01s
0m04.48s | categories/Category/Sigma/OnMorphisms                    | 0m04.42s
0m04.46s | categories/DualFunctor                                   | 0m04.48s
0m03.56s | categories/ProductLaws                                   | 0m03.64s
0m03.36s | types/ObjectClassifier                                   | 0m03.33s
0m03.11s | types/Sigma                                              | 0m03.00s
0m02.84s | categories/Functor/Prod/Functorial                       | 0m02.85s
0m02.84s | categories/Adjoint/UniversalMorphisms                    | 0m02.92s
0m02.67s | categories/FunctorCategory/Functorial                    | 0m02.60s
0m02.58s | categories/Grothendieck/ToSet                            | 0m02.45s
0m02.54s | Equivalences                                             | 0m02.53s
0m02.21s | categories/Functor/Attributes                            | 0m02.16s
0m02.20s | categories/Category/Sum                                  | 0m02.26s
0m02.10s | categories/Comma/Core                                    | 0m02.30s
0m02.00s | categories/Category/Sigma/Core                           | 0m02.04s
0m01.90s | PathGroupoids                                            | 0m01.79s
0m01.90s | categories/NaturalTransformation/Isomorphisms            | 0m01.88s
0m01.86s | categories/NaturalTransformation/Dual                    | 0m01.82s
0m01.83s | categories/Structure/Core                                |   N/A
0m01.72s | categories/HomFunctor                                    | 0m01.79s
0m01.69s | categories/FunctorCategory/Morphisms                     | 0m01.70s
0m01.63s | categories/NaturalTransformation/Paths                   | 0m01.59s
0m01.28s | types/Prod                                               | 0m01.29s
0m01.26s | categories/NaturalTransformation/Pointwise               | 0m01.35s
0m01.26s | categories/Category/Sigma/OnObjects                      | 0m01.25s
0m01.22s | categories/Category/Prod                                 | 0m01.25s
0m01.20s | categories/Limits/Core                                   | 0m01.12s
0m01.12s | categories/NaturalTransformation/Composition/Laws        | 0m01.16s
0m01.10s | categories/Functor/Pointwise                             | 0m01.07s
0m01.05s | categories/ExponentialLaws/Law  N/A                      | 0m01.07s
0m01.00s | categories/ExponentialLaws/Law1/Functors                 | 0m01.04s
0m00.97s | categories/CategoryOfSections/Core                       | 0m01.05s
0m00.96s | hit/epi                                                  | 0m00.86s
0m00.96s | categories/NaturalTransformation/Prod                    | 0m01.08s
0m00.84s | categories/Functor/Prod                                  | 0m00.84s
0m00.83s | hit/Spheres                                              | 0m00.95s
0m00.81s | categories/Functor/Composition/Functorial                | 0m00.89s
0m00.80s | types/Paths                                              | 0m00.86s
0m00.77s | Trunc                                                    | 0m00.77s
0m00.65s | types/Universe                                           | 0m00.64s
0m00.64s | categories/InitialTerminalCategory                       | 0m00.65s
0m00.64s | categories/NaturalTransformation/Composition/Core        | 0m00.63s
0m00.61s | contrib/HoTTBookExercises                                | 0m00.59s
0m00.56s | types/Sum                                                | 0m00.60s
0m00.56s | hit/quotient                                             | 0m00.56s
0m00.53s | hit/Suspension                                           | 0m00.57s
0m00.51s | Functorish                                               | 0m00.49s
0m00.51s | categories/NaturalTransformation/Sum                     | 0m00.56s
0m00.51s | categories/categories                                    | 0m00.58s
0m00.50s | categories/Limits/Functors                               | 0m00.47s
0m00.48s | types/Record                                             | 0m00.48s
0m00.48s | categories/Functor/Composition/Laws                      | 0m00.52s
0m00.47s | Tactics                                                  | 0m00.42s
0m00.46s | categories/ExponentialLaws/Law3/Functors                 | 0m00.45s
0m00.46s | hit/Circle                                               | 0m00.48s
0m00.46s | categories/KanExtensions/Functors                        | 0m00.46s
0m00.46s | categories/Comma/Projection                              | 0m00.50s
0m00.45s | HSet                                                     | 0m00.44s
0m00.42s | HProp                                                    | 0m00.41s
0m00.41s | categories/Functor/Functor                               | 0m00.31s
0m00.41s | categories/NaturalTransformation/Identity                | 0m00.42s
0m00.40s | categories/Cat/Core                                      | 0m00.46s
0m00.38s | types/Forall                                             | 0m00.47s
0m00.37s | TruncType                                                | 0m00.39s
0m00.34s | categories/Cat/Morphisms                                 | 0m00.30s
0m00.34s | Fibrations                                               | 0m00.36s
0m00.31s | categories/Functor/Dual                                  | 0m00.27s
0m00.30s | categories/IndiscreteCategory                            | 0m00.25s
0m00.29s | categories/NaturalTransformation/Composition/Functorial  | 0m00.30s
0m00.28s | categories/KanExtensions/Core                            | 0m00.25s
0m00.27s | categories/ExponentialLaws/ExponentialLaws               | 0m00.23s
0m00.27s | types/Arrow                                              | 0m00.25s
0m00.26s | hit/minus1Trunc                                          | 0m00.26s
0m00.25s | categories/Category/Objects                              | 0m00.24s
0m00.24s | Misc                                                     | 0m00.27s
0m00.24s | categories/Pseudofunctor/Pseudofunctor                   | 0m00.16s
0m00.24s | categories/Grothendieck/Grothendieck                     | 0m00.25s
0m00.23s | categories/Functor/Composition/Core                      | 0m00.22s
0m00.21s | categories/DependentProduct                              | 0m00.21s
0m00.21s | categories/Grothendieck/ToCat                            | 0m00.20s
0m00.21s | categories/Utf8                                          | 0m00.22s
0m00.21s | categories/Adjoint/Adjoint                               | 0m00.21s
0m00.20s | categories/NaturalTransformation/NaturalTransformation   | 0m00.21s
0m00.20s | categories/FunctorCategory/FunctorCategory               | 0m00.18s
0m00.20s | types/Bool                                               | 0m00.22s
0m00.19s | Conjugation                                              | 0m00.18s
0m00.19s | categories/NatCategory                                   | 0m00.15s
0m00.18s | categories/KanExtensions/KanExtensions                   | 0m00.16s
0m00.18s | categories/Profunctor/Core                               | 0m00.13s
0m00.18s | categories/Functor/Prod/Prod                             | 0m00.16s
0m00.18s | categories/SetCategory/Functors/Functors                 | 0m00.18s
0m00.18s | HoTT                                                     | 0m00.17s
0m00.18s | categories/Comma/Comma                                   | 0m00.19s
0m00.18s | categories/GroupoidCategory/Core                         | 0m00.17s
0m00.18s | categories/Notations                                     | 0m00.23s
0m00.18s | categories/NaturalTransformation/Notations               | 0m00.15s
0m00.18s | Overture                                                 | 0m00.14s
0m00.17s | categories/Limits/Limits                                 | 0m00.15s
0m00.17s | categories/FunctorCategory/Core                          | 0m00.18s
0m00.16s | categories/FunctorCategory/Utf8                          | 0m00.18s
0m00.16s | categories/Category/Dual                                 | 0m00.13s
0m00.16s | categories/Category/Univalent                            | 0m00.14s
0m00.16s | categories/Profunctor/Identity                           | 0m00.12s
0m00.15s | categories/Adjoint/Utf8                                  | 0m00.16s
0m00.15s | hit/iso                                                  | 0m00.19s
0m00.15s | categories/Profunctor/Representable                      | 0m00.17s
0m00.15s | FunextVarieties                                          | 0m00.20s
0m00.14s | categories/Cat/Cat                                       | 0m00.16s
0m00.14s | contrib/HoTTBook                                         | 0m00.13s
0m00.14s | hit/Interval                                             | 0m00.11s
0m00.14s | categories/SetCategory/Core                              | 0m00.12s
0m00.14s | categories/Adjoint/Identity                              | 0m00.18s
0m00.14s | categories/Functor/Notations                             | 0m00.18s
0m00.14s | categories/Category/Category                             | 0m00.15s
0m00.14s | categories/Adjoint/Composition/Composition               | 0m00.13s
0m00.14s | categories/NaturalTransformation/Core                    | 0m00.15s
0m00.14s | categories/Functor/Utf8                                  | 0m00.17s
0m00.14s | categories/ExponentialLaws/Law1/Law1                     | 0m00.16s
0m00.14s | categories/NaturalTransformation/Utf8                    | 0m00.18s
0m00.14s | hit/Truncations                                          | 0m00.13s
0m00.14s | categories/Adjoint/Composition/LawsTactic                | 0m00.16s
0m00.13s | hit/unique_choice                                        | 0m00.12s
0m00.13s | categories/Adjoint/Notations                             | 0m00.16s
0m00.13s | categories/Comma/Notations                               | 0m00.14s
0m00.13s | categories/Category/Core                                 | 0m00.14s
0m00.13s | categories/ExponentialLaws/Law2/Law2                     | 0m00.18s
0m00.13s | categories/Functor/Composition/Composition               | 0m00.11s
0m00.12s | categories/ExponentialLaws/Law3/Law3                     | 0m00.13s
0m00.12s | categories/GroupoidCategory/GroupoidCategory             | 0m00.13s
0m00.12s | categories/Category/Utf8                                 | 0m00.10s
0m00.12s | categories/ExponentialLaws/Law4/Law4                     | 0m00.08s
0m00.12s | categories/Profunctor/Profunctor                         | 0m00.16s
0m00.12s | categories/Category/Subcategory/Wide                     | 0m00.12s
0m00.12s | hit/TwoSphere                                            | 0m00.12s
0m00.12s | categories/SetCategory/SetCategory                       | 0m00.13s
0m00.12s | types/Unit                                               | 0m00.14s
0m00.11s | categories/Comma/Utf8                                    | 0m00.14s
0m00.11s | categories/DiscreteCategory                              | 0m00.10s
0m00.11s | categories/Adjoint/Core                                  | 0m00.13s
0m00.11s | Contractible                                             | 0m00.12s
0m00.11s | categories/Category/Sigma/Sigma                          | 0m00.12s
0m00.11s | categories/Category/Subcategory/Full                     | 0m00.12s
0m00.11s | categories/FunctorCategory/Notations                     | 0m00.14s
0m00.11s | categories/Profunctor/Utf8                               | 0m00.12s
0m00.11s | categories/CategoryOfSections/CategoryOfSections         | 0m00.09s
0m00.10s | categories/Profunctor/Notations                          | 0m00.10s
0m00.10s | categories/Functor/Core                                  | 0m00.08s
0m00.10s | categories/Structure/Utf8                                |   N/A
0m00.10s | categories/Category/Subcategory/Subcategory              | 0m00.12s
0m00.10s | Pointed                                                  | 0m00.07s
0m00.10s | categories/Category/Notations                            | 0m00.13s
0m00.10s | categories/Functor/Pointwise/Pointwise                   | 0m00.11s
0m00.10s | types/Empty                                              | 0m00.06s
0m00.09s | coq/Init/Peano                                           | 0m00.13s
0m00.09s | categories/Structure/Notations                           |   N/A
0m00.09s | categories/NaturalTransformation/Composition/Composition | 0m00.11s
0m00.08s | categories/Functor/Identity                              | 0m00.08s
0m00.08s | categories/Category/Strict                               | 0m00.07s
0m00.08s | coq/Init/Specif                                          | 0m00.06s
0m00.08s | categories/Structure/Structure                           |   N/A
0m00.07s | types/UniverseLevel                                      | 0m00.09s
0m00.07s | coq/Init/Logic_Type                                      | 0m00.06s
0m00.06s | coq/Init/Datatypes                                       | 0m00.06s
0m00.06s | UnivalenceAxiom                                          | 0m00.07s
0m00.06s | FunextAxiom                                              | 0m00.08s
0m00.04s | coq/Init/Notations                                       | 0m00.04s
0m00.04s | coq/Init/Prelude                                         | 0m00.02s
0m00.04s | coq/Init/Tactics                                         | 0m00.03s
0m00.04s | coq/Program/Tactics                                      | 0m00.06s
0m00.03s | coq/Init/Logic                                           | 0m00.02s
0m00.02s | coq/Bool/Bool                                            | 0m00.04s
Formalize the structure identity principle

After    | File Name                                                | Before
------------------------------------------------------------------------------
8m41.47s | Total                                                    | 8m27.02s
------------------------------------------------------------------------------
1m45.29s | categories/Comma/ProjectionFunctors                      | 1m45.27s
0m34.19s | categories/Adjoint/Composition/AssociativityLaw          | 0m32.58s
0m25.49s | categories/Grothendieck/PseudofunctorToCat               | 0m24.22s
0m17.40s | categories/ExponentialLaws/Law4/Functors                 | 0m16.19s
0m16.70s | categories/Adjoint/UnitCounitCoercions                   | 0m16.97s
0m16.69s | categories/Comma/InducedFunctors                         | 0m15.71s
0m15.89s | categories/FunctorCategory/Dual                          | 0m16.11s
0m13.50s | categories/Adjoint/Composition/Core                      | 0m12.01s
0m12.84s | hit/Flattening                                           | 0m12.81s
0m12.65s | categories/Adjoint/Dual                                  | 0m11.56s
0m12.30s | categories/Functor/Pointwise/Properties                  | 0m13.01s
0m12.09s | categories/Pseudofunctor/Core                            | 0m13.43s
0m11.92s | categories/Pseudofunctor/FromFunctor                     | 0m10.85s
0m11.35s | categories/Adjoint/Composition/IdentityLaws              | 0m10.84s
0m09.15s | categories/Yoneda                                        | 0m07.86s
0m08.10s | categories/ExponentialLaws/Law1/Law                      | 0m07.98s
0m08.02s | categories/Functor/Prod/Universal                        | 0m08.03s
0m08.02s | categories/GroupoidCategory/Morphisms                    | 0m07.56s
0m06.87s | categories/Adjoint/Paths                                 | 0m06.82s
0m06.83s | hit/Connectedness                                        | 0m07.11s
0m06.46s | categories/Structure/IdentityPrinciple                   |   N/A
0m06.44s | categories/UniversalProperties                           | 0m07.29s
0m06.23s | categories/Comma/Dual                                    | 0m06.77s
0m06.06s | categories/Adjoint/UnitCounit                            | 0m06.96s
0m06.04s | categories/Category/Morphisms                            | 0m05.68s
0m05.84s | categories/Functor/Paths                                 | 0m06.26s
0m05.67s | categories/Functor/Sum                                   | 0m05.70s
0m05.28s | EquivalenceVarieties                                     | 0m05.49s
0m04.89s | categories/ExponentialLaws/Law2/Functors                 | 0m04.89s
0m04.63s | categories/DualFunctor                                   | 0m05.16s
0m04.48s | categories/Category/Sigma/OnMorphisms                    | 0m04.40s
0m03.80s | categories/ProductLaws                                   | 0m03.57s
0m03.50s | types/ObjectClassifier                                   | 0m03.40s
0m03.49s | categories/Structure/Core                                | 0m01.76s
0m03.07s | types/Sigma                                              | 0m03.03s
0m02.85s | categories/Functor/Prod/Functorial                       | 0m03.32s
0m02.76s | categories/Adjoint/UniversalMorphisms                    | 0m02.91s
0m02.62s | categories/FunctorCategory/Functorial                    | 0m02.56s
0m02.62s | Equivalences                                             | 0m02.51s
0m02.50s | categories/Grothendieck/ToSet                            | 0m02.39s
0m02.38s | categories/Functor/Attributes                            | 0m02.42s
0m02.27s | categories/Category/Sum                                  | 0m02.20s
0m02.06s | categories/Comma/Core                                    | 0m01.98s
0m02.01s | categories/Category/Sigma/Core                           | 0m02.07s
0m01.90s | PathGroupoids                                            | 0m01.93s
0m01.84s | categories/HomFunctor                                    | 0m01.86s
0m01.84s | categories/NaturalTransformation/Isomorphisms            | 0m01.88s
0m01.83s | categories/NaturalTransformation/Dual                    | 0m01.80s
0m01.76s | categories/FunctorCategory/Morphisms                     | 0m01.74s
0m01.65s | categories/NaturalTransformation/Paths                   | 0m01.72s
0m01.34s | categories/NaturalTransformation/Pointwise               | 0m01.30s
0m01.30s | categories/Category/Sigma/OnObjects                      | 0m01.25s
0m01.29s | categories/Category/Prod                                 | 0m01.31s
0m01.26s | types/Prod                                               | 0m01.27s
0m01.26s | categories/NaturalTransformation/Composition/Laws        | 0m01.21s
0m01.20s | categories/Functor/Pointwise                             | 0m01.07s
0m01.16s | categories/Limits/Core                                   | 0m01.26s
0m01.08s | categories/ExponentialLaws/Law  N/A                      | 0m00.98s
0m01.06s | categories/CategoryOfSections/Core                       | 0m01.01s
0m01.05s | hit/Spheres                                              | 0m00.93s
0m01.05s | categories/ExponentialLaws/Law1/Functors                 | 0m00.89s
0m00.93s | hit/epi                                                  | 0m01.02s
0m00.91s | categories/NaturalTransformation/Prod                    | 0m01.00s
0m00.89s | categories/Functor/Composition/Functorial                | 0m00.82s
0m00.86s | categories/Functor/Prod                                  | 0m00.90s
0m00.83s | types/Paths                                              | 0m00.90s
0m00.80s | Trunc                                                    | 0m00.81s
0m00.66s | categories/NaturalTransformation/Composition/Core        | 0m00.65s
0m00.65s | contrib/HoTTBookExercises                                | 0m00.62s
0m00.62s | categories/InitialTerminalCategory                       | 0m00.69s
0m00.61s | types/Universe                                           | 0m00.66s
0m00.59s | types/Sum                                                | 0m00.58s
0m00.59s | hit/quotient                                             | 0m00.53s
0m00.57s | categories/categories                                    | 0m00.53s
0m00.56s | Functorish                                               | 0m00.63s
0m00.56s | hit/Circle                                               | 0m00.56s
0m00.51s | types/Record                                             | 0m00.46s
0m00.51s | categories/Functor/Composition/Laws                      | 0m00.52s
0m00.50s | categories/NaturalTransformation/Sum                     | 0m00.52s
0m00.49s | hit/Suspension                                           | 0m00.51s
0m00.48s | HProp                                                    | 0m00.41s
0m00.48s | categories/KanExtensions/Functors                        | 0m00.45s
0m00.48s | categories/Comma/Projection                              | 0m00.56s
0m00.46s | HSet                                                     | 0m00.45s
0m00.44s | categories/Cat/Core                                      | 0m00.43s
0m00.44s | categories/Functor/Functor                               | 0m00.33s
0m00.44s | types/Forall                                             | 0m00.37s
0m00.43s | Tactics                                                  | 0m00.40s
0m00.42s | categories/Limits/Functors                               | 0m00.44s
0m00.41s | categories/ExponentialLaws/Law3/Functors                 | 0m00.45s
0m00.39s | Fibrations                                               | 0m00.39s
0m00.38s | categories/NaturalTransformation/Identity                | 0m00.43s
0m00.34s | categories/IndiscreteCategory                            | 0m00.24s
0m00.34s | TruncType                                                | 0m00.36s
0m00.32s | categories/Functor/Dual                                  | 0m00.31s
0m00.32s | categories/KanExtensions/Core                            | 0m00.28s
0m00.30s | Misc                                                     | 0m00.28s
0m00.30s | categories/NaturalTransformation/Composition/Functorial  | 0m00.26s
0m00.29s | categories/Cat/Morphisms                                 | 0m00.28s
0m00.28s | categories/ExponentialLaws/ExponentialLaws               | 0m00.28s
0m00.27s | hit/minus1Trunc                                          | 0m00.24s
0m00.26s | categories/Category/Objects                              | 0m00.25s
0m00.26s | types/Arrow                                              | 0m00.30s
0m00.25s | categories/FunctorCategory/Utf8                          | 0m00.14s
0m00.23s | categories/Functor/Composition/Core                      | 0m00.22s
0m00.22s | categories/Comma/Comma                                   | 0m00.18s
0m00.22s | categories/NatCategory                                   | 0m00.16s
0m00.22s | categories/Adjoint/Adjoint                               | 0m00.22s
0m00.22s | types/Bool                                               | 0m00.21s
0m00.22s | categories/Grothendieck/Grothendieck                     | 0m00.26s
0m00.20s | Conjugation                                              | 0m00.19s
0m00.20s | contrib/HoTTBook                                         | 0m00.17s
0m00.20s | categories/GroupoidCategory/Core                         | 0m00.17s
0m00.20s | categories/Notations                                     | 0m00.24s
0m00.20s | categories/ExponentialLaws/Law1/Law1                     | 0m00.17s
0m00.20s | categories/FunctorCategory/Core                          | 0m00.17s
0m00.19s | categories/Adjoint/Notations                             | 0m00.17s
0m00.19s | categories/Utf8                                          | 0m00.24s
0m00.18s | categories/ExponentialLaws/Law3/Law3                     | 0m00.16s
0m00.18s | categories/DependentProduct                              | 0m00.21s
0m00.18s | categories/NaturalTransformation/NaturalTransformation   | 0m00.18s
0m00.18s | categories/Functor/Prod/Prod                             | 0m00.19s
0m00.18s | categories/SetCategory/Functors/Functors                 | 0m00.26s
0m00.18s | HoTT                                                     | 0m00.21s
0m00.18s | categories/Category/Dual                                 | 0m00.14s
0m00.18s | categories/Grothendieck/ToCat                            | 0m00.20s
0m00.18s | categories/FunctorCategory/FunctorCategory               | 0m00.15s
0m00.18s | categories/Pseudofunctor/Pseudofunctor                   | 0m00.15s
0m00.18s | FunextVarieties                                          | 0m00.18s
0m00.17s | categories/Functor/Notations                             | 0m00.14s
0m00.16s | categories/Comma/Utf8                                    | 0m00.14s
0m00.16s | categories/Adjoint/Utf8                                  | 0m00.16s
0m00.16s | categories/KanExtensions/KanExtensions                   | 0m00.14s
0m00.16s | categories/Cat/Cat                                       | 0m00.20s
0m00.16s | categories/SetCategory/Core                              | 0m00.12s
0m00.16s | categories/ExponentialLaws/Law4/Law4                     | 0m00.13s
0m00.16s | categories/Comma/Notations                               | 0m00.20s
0m00.16s | categories/NaturalTransformation/Core                    | 0m00.15s
0m00.16s | categories/Functor/Utf8                                  | 0m00.17s
0m00.16s | categories/NaturalTransformation/Notations               | 0m00.18s
0m00.16s | categories/Category/Core                                 | 0m00.17s
0m00.16s | categories/NaturalTransformation/Utf8                    | 0m00.15s
0m00.15s | hit/iso                                                  | 0m00.18s
0m00.15s | categories/Adjoint/Identity                              | 0m00.11s
0m00.15s | categories/Category/Category                             | 0m00.12s
0m00.15s | categories/Adjoint/Composition/Composition               | 0m00.15s
0m00.15s | categories/Profunctor/Representable                      | 0m00.17s
0m00.15s | types/Unit                                               | 0m00.16s
0m00.15s | Overture                                                 | 0m00.15s
0m00.14s | categories/DiscreteCategory                              | 0m00.06s
0m00.14s | categories/Limits/Limits                                 | 0m00.17s
0m00.14s | categories/Profunctor/Core                               | 0m00.13s
0m00.14s | hit/unique_choice                                        | 0m00.12s
0m00.14s | categories/Profunctor/Profunctor                         | 0m00.17s
0m00.14s | hit/TwoSphere                                            | 0m00.14s
0m00.14s | categories/Functor/Composition/Composition               | 0m00.15s
0m00.14s | categories/Adjoint/Composition/LawsTactic                | 0m00.09s
0m00.13s | hit/Truncations                                          | 0m00.13s
0m00.12s | categories/GroupoidCategory/GroupoidCategory             | 0m00.12s
0m00.12s | hit/Interval                                             | 0m00.14s
0m00.12s | categories/Structure/Structure                           | 0m00.10s
0m00.12s | categories/Functor/Core                                  | 0m00.10s
0m00.12s | categories/Category/Univalent                            | 0m00.13s
0m00.12s | categories/Profunctor/Identity                           | 0m00.14s
0m00.12s | categories/Category/Sigma/Sigma                          | 0m00.12s
0m00.12s | categories/ExponentialLaws/Law2/Law2                     | 0m00.12s
0m00.12s | categories/Functor/Pointwise/Pointwise                   | 0m00.14s
0m00.12s | categories/CategoryOfSections/CategoryOfSections         | 0m00.08s
0m00.11s | categories/Category/Utf8                                 | 0m00.11s
0m00.11s | categories/Profunctor/Notations                          | 0m00.11s
0m00.11s | categories/Category/Subcategory/Subcategory              | 0m00.12s
0m00.11s | categories/Category/Notations                            | 0m00.10s
0m00.11s | categories/NaturalTransformation/Composition/Composition | 0m00.12s
0m00.11s | categories/FunctorCategory/Notations                     | 0m00.12s
0m00.11s | categories/Structure/Utf8                                | 0m00.10s
0m00.11s | categories/Profunctor/Utf8                               | 0m00.12s
0m00.10s | categories/Adjoint/Core                                  | 0m00.10s
0m00.10s | coq/Init/Peano                                           | 0m00.10s
0m00.10s | Pointed                                                  | 0m00.08s
0m00.09s | Contractible                                             | 0m00.09s
0m00.09s | categories/Category/Strict                               | 0m00.07s
0m00.09s | categories/Category/Subcategory/Wide                     | 0m00.07s
0m00.09s | UnivalenceAxiom                                          | 0m00.10s
0m00.09s | categories/Category/Subcategory/Full                     | 0m00.08s
0m00.08s | categories/Structure/Notations                           | 0m00.09s
0m00.08s | types/UniverseLevel                                      | 0m00.06s
0m00.08s | categories/SetCategory/SetCategory                       | 0m00.08s
0m00.08s | coq/Program/Tactics                                      | 0m00.07s
0m00.07s | categories/Functor/Identity                              | 0m00.08s
0m00.06s | coq/Init/Datatypes                                       | 0m00.07s
0m00.06s | FunextAxiom                                              | 0m00.06s
0m00.06s | types/Empty                                              | 0m00.09s
0m00.05s | coq/Init/Specif                                          | 0m00.09s
0m00.05s | coq/Init/Logic_Type                                      | 0m00.06s
0m00.04s | coq/Init/Notations                                       | 0m00.03s
0m00.04s | coq/Init/Logic                                           | 0m00.02s
0m00.04s | coq/Init/Prelude                                         | 0m00.03s
0m00.02s | coq/Bool/Bool                                            | 0m00.04s
0m00.02s | coq/Init/Tactics                                         | 0m00.04s
Connect up SIP to the book
Tie in the extant category theory with the book
Merge pull request #350 from JasonGross/structure-identity-principle

Structure identity principle
Add many variants of the [simpl rewrite] tactic

It's unfortunate that Coq doesn't give us a notation of saying "this
takes anything that rewrite can take".  But these are useful for
making tactic scripts conceptually clearer.
Define a variant of [path_sigma] for hprops

In this case, we don't need to provide the second projection.

Also prove that it's an equivalence.
Define the hom-set adjunction

Prove that it's logically equivalent to the other kinds of adjunctions
(via a coercion to the adjunction-unit definition).

There's not too much going on in the proof scripts, but maybe someone
can find a way to make them even cleaner?