Prove functoriality of comma category construction

At least in its category arguments.

This is the first step in showing that two formulations of (co)limits
are equivalent.

Unfortunately, it's somewhat slow.  Ideas for speeding it up are welcome.

After    | File Name                                                          | Before   || Change
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6m13.31s | Total                                                              | 6m24.93s || -0m11.61s
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0m16.07s | categories/Comma/Functorial                                        |   N/A    || +0m16.07s
1m01.86s | categories/Pseudofunctor/RewriteLaws                               | 1m05.20s || -0m03.34s
0m08.51s | categories/FunctorCategory/Dual                                    | 0m11.78s || -0m03.26s
0m06.94s | categories/Adjoint/UnitCounit                                      | 0m09.70s || -0m02.75s
0m17.63s | categories/ExponentialLaws/Law4/Functors                           | 0m19.54s || -0m01.91s
0m12.28s | categories/Comma/InducedFunctors                                   | 0m13.52s || -0m01.24s
0m11.26s | categories/PseudonaturalTransformation/Core                        | 0m12.59s || -0m01.33s
0m09.36s | categories/Adjoint/Composition/AssociativityLaw                    | 0m10.56s || -0m01.20s
0m08.34s | categories/Yoneda                                                  | 0m09.96s || -0m01.62s
0m04.36s | categories/Pseudofunctor/Identity                                  | 0m05.72s || -0m01.35s
0m04.35s | categories/Pseudofunctor/FromFunctor                               | 0m06.04s || -0m01.69s
0m39.15s | categories/Comma/ProjectionFunctors                                | 0m38.68s || +0m00.46s
0m22.02s | categories/Grothendieck/PseudofunctorToCat                         | 0m22.53s || -0m00.51s
0m12.25s | categories/Adjoint/Dual                                            | 0m11.85s || +0m00.40s
0m07.06s | categories/Adjoint/HomCoercions                                    | 0m07.16s || -0m00.10s
0m05.98s | categories/UniversalProperties                                     | 0m06.37s || -0m00.38s
0m04.87s | categories/Adjoint/UnitCounitCoercions                             | 0m05.19s || -0m00.32s
0m03.82s | categories/Pseudofunctor/Core                                      | 0m04.36s || -0m00.54s
0m03.66s | categories/Adjoint/Composition/IdentityLaws                        | 0m04.14s || -0m00.47s
0m03.47s | categories/Comma/Dual                                              | 0m03.80s || -0m00.32s
0m03.30s | categories/GroupoidCategory/Morphisms                              | 0m03.62s || -0m00.32s
0m03.27s | categories/Adjoint/Composition/Core                                | 0m03.03s || +0m00.24s
0m03.23s | categories/Structure/IdentityPrinciple                             | 0m03.53s || -0m00.29s
0m03.19s | categories/Functor/Pointwise/Properties                            | 0m03.52s || -0m00.33s
0m03.10s | categories/Category/Morphisms                                      | 0m03.26s || -0m00.15s
0m03.07s | categories/Adjoint/UniversalMorphisms                              | 0m03.43s || -0m00.36s
0m02.75s | categories/ExponentialLaws/Law1/Law                                | 0m02.84s || -0m00.08s
0m02.65s | hit/Flattening                                                     | 0m02.97s || -0m00.32s
0m02.58s | categories/Functor/Composition/Functorial/Core                     | 0m03.11s || -0m00.52s
0m02.45s | categories/Limits/Core                                             | 0m03.35s || -0m00.89s
0m02.40s | categories/Functor/Prod/Functorial                                 | 0m01.98s || +0m00.41s
0m02.12s | categories/ProductLaws                                             | 0m01.72s || +0m00.40s
0m02.11s | categories/Functor/Composition/Functorial/Attributes               | 0m02.31s || -0m00.20s
0m01.85s | categories/ExponentialLaws/Law2/Functors                           | 0m01.84s || +0m00.01s
0m01.81s | categories/Category/Sigma/OnMorphisms                              | 0m01.86s || -0m00.05s
0m01.80s | categories/Functor/Prod/Universal                                  | 0m02.04s || -0m00.24s
0m01.79s | categories/Functor/Attributes                                      | 0m02.14s || -0m00.35s
0m01.74s | hit/Connectedness                                                  | 0m01.74s || +0m00.00s
0m01.60s | categories/ExponentialLaws/Law  N/A                                | 0m01.54s || +0m00.06s
0m01.59s | categories/NaturalTransformation/Isomorphisms                      | 0m01.79s || -0m00.19s
0m01.53s | categories/Functor/Sum                                             | 0m01.55s || -0m00.02s
0m01.46s | categories/Limits/Functors                                         | 0m01.46s || +0m00.00s
0m01.44s | categories/NaturalTransformation/Pointwise                         | 0m01.73s || -0m00.29s
0m01.44s | categories/InitialTerminalCategory/Pseudofunctors                  | 0m01.62s || -0m00.18s
0m01.44s | categories/Functor/Paths                                           | 0m01.66s || -0m00.21s
0m01.31s | categories/Functor/Pointwise                                       | 0m01.51s || -0m00.19s
0m01.25s | categories/FunctorCategory/Functorial                              | 0m01.50s || -0m00.25s
0m01.25s | categories/Category/Sum                                            | 0m01.24s || +0m00.01s
0m01.21s | Equivalences                                                       | 0m01.22s || -0m00.01s
0m01.20s | categories/ExponentialLaws/Law1/Functors                           | 0m01.26s || -0m00.06s
0m01.18s | HProp                                                              | 0m01.14s || +0m00.04s
0m01.17s | categories/Adjoint/Paths                                           | 0m01.31s || -0m00.14s
0m01.16s | HSet                                                               | 0m01.23s || -0m00.07s
0m01.15s | categories/KanExtensions/Functors                                  | 0m01.05s || +0m00.09s
0m01.12s | types/Sigma                                                        | 0m01.11s || +0m00.01s
0m01.12s | categories/DualFunctor                                             | 0m01.39s || -0m00.26s
0m01.09s | categories/FunctorCategory/Morphisms                               | 0m01.26s || -0m00.16s
0m01.00s | PathGroupoids                                                      | 0m01.02s || -0m00.02s
0m00.95s | types/Record                                                       | 0m00.96s || -0m00.01s
0m00.93s | categories/Structure/Core                                          | 0m00.99s || -0m00.05s
0m00.89s | categories/Comma/Core                                              | 0m00.92s || -0m00.03s
0m00.84s | categories/Functor/Prod                                            | 0m00.83s || +0m00.01s
0m00.82s | EquivalenceVarieties                                               | 0m00.92s || -0m00.10s
0m00.82s | types/ObjectClassifier                                             | 0m00.82s || +0m00.00s
0m00.81s | categories/Category/Sigma/Core                                     | 0m00.87s || -0m00.05s
0m00.80s | categories/HomFunctor                                              | 0m00.84s || -0m00.03s
0m00.76s | categories/NaturalTransformation/Prod                              | 0m00.85s || -0m00.08s
0m00.75s | categories/Grothendieck/ToCat                                      | 0m00.78s || -0m00.03s
0m00.67s | categories/Category/Prod                                           | 0m00.68s || -0m00.01s
0m00.65s | categories/Category/Sigma/OnObjects                                | 0m00.70s || -0m00.04s
0m00.61s | categories/Grothendieck/ToSet                                      | 0m00.70s || -0m00.08s
0m00.58s | hit/Spheres                                                        | 0m00.64s || -0m00.06s
0m00.58s | categories/KanExtensions/Core                                      | 0m00.56s || +0m00.01s
0m00.55s | categories/categories                                              | 0m00.50s || +0m00.05s
0m00.54s | types/Prod                                                         | 0m00.53s || +0m00.01s
0m00.54s | categories/NaturalTransformation/Dual                              | 0m00.53s || +0m00.01s
0m00.52s | contrib/HoTTBook                                                   | 0m00.49s || +0m00.03s
0m00.52s | types/Paths                                                        | 0m00.51s || +0m00.01s
0m00.51s | contrib/HoTTBookExercises                                          | 0m00.52s || -0m00.01s
0m00.50s | categories/Comma/Projection                                        | 0m00.43s || +0m00.07s
0m00.49s | categories/SetCategory/Morphisms                                   | 0m00.52s || -0m00.03s
0m00.47s | categories/ExponentialLaws/Law3/Functors                           | 0m00.42s || +0m00.04s
0m00.45s | categories/CategoryOfSections/Core                                 | 0m00.41s || +0m00.04s
0m00.44s | categories/InitialTerminalCategory/Functors                        | 0m00.43s || +0m00.01s
0m00.43s | hit/epi                                                            | 0m00.44s || -0m00.01s
0m00.43s | categories/NaturalTransformation/Composition/Laws                  | 0m00.41s || +0m00.02s
0m00.43s | hit/Circle                                                         | 0m00.44s || -0m00.01s
0m00.40s | categories/NaturalTransformation/Paths                             | 0m00.48s || -0m00.07s
0m00.34s | types/Sum                                                          | 0m00.36s || -0m00.01s
0m00.33s | categories/NaturalTransformation/Sum                               | 0m00.31s || +0m00.02s
0m00.32s | types/Universe                                                     | 0m00.38s || -0m00.06s
0m00.30s | categories/IndiscreteCategory                                      | 0m00.36s || -0m00.06s
0m00.30s | hit/Suspension                                                     | 0m00.28s || +0m00.01s
0m00.30s | Tactics                                                            | 0m00.30s || +0m00.00s
0m00.30s | hit/quotient                                                       | 0m00.38s || -0m00.08s
0m00.30s | categories/NaturalTransformation/Composition/Functorial            | 0m00.31s || -0m00.01s
0m00.30s | Fibrations                                                         | 0m00.29s || +0m00.01s
0m00.29s | categories/DependentProduct                                        | 0m00.28s || +0m00.00s
0m00.28s | types/Forall                                                       | 0m00.25s || +0m00.03s
0m00.27s | categories/Cat/Core                                                | 0m00.30s || -0m00.02s
0m00.26s | categories/ExponentialLaws/ExponentialLaws                         | 0m00.22s || +0m00.04s
0m00.26s | categories/InitialTerminalCategory/NaturalTransformations          | 0m00.18s || +0m00.08s
0m00.26s | categories/Functor/Functor                                         | 0m00.22s || +0m00.04s
0m00.25s | Trunc                                                              | 0m00.28s || -0m00.03s
0m00.25s | hit/minus1Trunc                                                    | 0m00.22s || +0m00.03s
0m00.25s | categories/Functor/Composition/Laws                                | 0m00.24s || +0m00.01s
0m00.24s | categories/FundamentalPreGroupoidCategory                          | 0m00.25s || -0m00.01s
0m00.24s | Functorish                                                         | 0m00.25s || -0m00.01s
0m00.24s | categories/Notations                                               | 0m00.26s || -0m00.02s
0m00.24s | categories/Adjoint/Adjoint                                         | 0m00.22s || +0m00.01s
0m00.24s | categories/Cat/Morphisms                                           | 0m00.22s || +0m00.01s
0m00.23s | UnivalenceImpliesFunext                                            | 0m00.27s || -0m00.04s
0m00.23s | categories/Functor/Dual                                            | 0m00.18s || +0m00.05s
0m00.22s | categories/NaturalTransformation/Composition/Core                  | 0m00.25s || -0m00.03s
0m00.21s | categories/Adjoint/Hom                                             | 0m00.21s || +0m00.00s
0m00.21s | categories/Comma/Comma                                             | 0m00.13s || +0m00.07s
0m00.21s | categories/Functor/Notations                                       | 0m00.16s || +0m00.04s
0m00.21s | categories/NaturalTransformation/Identity                          | 0m00.20s || +0m00.00s
0m00.20s | TruncType                                                          | 0m00.29s || -0m00.08s
0m00.20s | categories/PseudonaturalTransformation/PseudonaturalTransformation | 0m00.13s || +0m00.07s
0m00.20s | categories/NaturalTransformation/Utf8                              | 0m00.18s || +0m00.02s
0m00.19s | categories/SetCategory/Functors/Functors                           | 0m00.18s || +0m00.01s
0m00.19s | categories/Functor/Composition/Composition                         | 0m00.19s || +0m00.00s
0m00.19s | types/Arrow                                                        | 0m00.19s || +0m00.00s
0m00.18s | categories/Category/Objects                                        | 0m00.16s || +0m00.01s
0m00.18s | categories/InitialTerminalCategory/InitialTerminalCategory         | 0m00.18s || +0m00.00s
0m00.18s | Overture                                                           | 0m00.18s || +0m00.00s
0m00.17s | categories/Functor/Composition/Functorial                          | 0m00.25s || -0m00.07s
0m00.17s | categories/NaturalTransformation/NaturalTransformation             | 0m00.20s || -0m00.03s
0m00.17s | categories/Functor/Prod/Prod                                       | 0m00.19s || -0m00.01s
0m00.17s | categories/CategoryOfGroupoids                                     | 0m00.22s || -0m00.04s
0m00.17s | categories/NatCategory                                             | 0m00.13s || +0m00.04s
0m00.17s | types/Bool                                                         | 0m00.20s || -0m00.03s
0m00.17s | categories/Grothendieck/Grothendieck                               | 0m00.14s || +0m00.03s
0m00.17s | categories/FunctorCategory/Core                                    | 0m00.18s || -0m00.00s
0m00.16s | categories/Limits/Limits                                           | 0m00.15s || +0m00.01s
0m00.16s | categories/InitialTerminalCategory/Notations                       | 0m00.14s || +0m00.01s
0m00.16s | categories/HomotopyPreCategory                                     | 0m00.16s || +0m00.00s
0m00.16s | categories/Category/Pi                                             | 0m00.12s || +0m00.04s
0m00.15s | categories/Cat/Cat                                                 | 0m00.15s || +0m00.00s
0m00.15s | categories/Structure/Structure                                     | 0m00.11s || +0m00.03s
0m00.15s | categories/Adjoint/Identity                                        | 0m00.12s || +0m00.03s
0m00.15s | categories/NaturalTransformation/Core                              | 0m00.18s || -0m00.03s
0m00.15s | Tests                                                              | 0m00.13s || +0m00.01s
0m00.14s | categories/Profunctor/Representable                                | 0m00.16s || -0m00.01s
0m00.14s | categories/Comma/Utf8                                              | 0m00.20s || -0m00.06s
0m00.14s | categories/KanExtensions/KanExtensions                             | 0m00.12s || +0m00.02s
0m00.14s | categories/FunctorCategory/Utf8                                    | 0m00.17s || -0m00.03s
0m00.14s | hit/Interval                                                       | 0m00.13s || +0m00.01s
0m00.14s | hit/iso                                                            | 0m00.15s || -0m00.00s
0m00.14s | HoTT                                                               | 0m00.21s || -0m00.06s
0m00.14s | Misc                                                               | 0m00.13s || +0m00.01s
0m00.14s | categories/InitialTerminalCategory/Core                            | 0m00.15s || -0m00.00s
0m00.14s | categories/FunctorCategory/FunctorCategory                         | 0m00.19s || -0m00.04s
0m00.14s | Modality                                                           | 0m00.17s || -0m00.03s
0m00.14s | categories/Utf8                                                    | 0m00.23s || -0m00.09s
0m00.14s | categories/GroupoidCategory/Core                                   | 0m00.18s || -0m00.03s
0m00.14s | categories/Functor/Utf8                                            | 0m00.18s || -0m00.03s
0m00.14s | categories/Pseudofunctor/Pseudofunctor                             | 0m00.17s || -0m00.03s
0m00.14s | categories/NaturalTransformation/Notations                         | 0m00.12s || +0m00.02s
0m00.14s | FunextVarieties                                                    | 0m00.15s || -0m00.00s
0m00.14s | categories/SetCategory/SetCategory                                 | 0m00.07s || +0m00.07s
0m00.14s | categories/Profunctor/Identity                                     | 0m00.14s || +0m00.00s
0m00.14s | categories/ExponentialLaws/Law1/Law1                               | 0m00.12s || +0m00.02s
0m00.13s | Conjugation                                                        | 0m00.14s || -0m00.01s
0m00.13s | categories/Profunctor/Profunctor                                   | 0m00.15s || -0m00.01s
0m00.13s | categories/Category/Category                                       | 0m00.11s || +0m00.02s
0m00.13s | types/Unit                                                         | 0m00.12s || +0m00.01s
0m00.13s | hit/Truncations                                                    | 0m00.11s || +0m00.02s
0m00.13s | categories/Adjoint/Composition/LawsTactic                          | 0m00.11s || +0m00.02s
0m00.12s | categories/ExponentialLaws/Law3/Law3                               | 0m00.13s || -0m00.01s
0m00.12s | categories/DiscreteCategory                                        | 0m00.12s || +0m00.00s
0m00.12s | Contractible                                                       | 0m00.11s || +0m00.00s
0m00.12s | categories/Adjoint/Notations                                       | 0m00.12s || +0m00.00s
0m00.12s | categories/Category/Univalent                                      | 0m00.11s || +0m00.00s
0m00.12s | categories/Comma/Notations                                         | 0m00.12s || +0m00.00s
0m00.12s | categories/Structure/Notations                                     | 0m00.10s || +0m00.01s
0m00.12s | categories/Profunctor/Utf8                                         | 0m00.14s || -0m00.02s
0m00.12s | categories/CategoryOfSections/CategoryOfSections                   | 0m00.12s || +0m00.00s
0m00.11s | categories/Adjoint/Core                                            | 0m00.08s || +0m00.03s
0m00.11s | hit/unique_choice                                                  | 0m00.12s || -0m00.00s
0m00.11s | categories/Adjoint/Composition/Composition                         | 0m00.12s || -0m00.00s
0m00.11s | categories/Category/Sigma/Sigma                                    | 0m00.08s || +0m00.03s
0m00.11s | categories/FunctorCategory/Notations                               | 0m00.14s || -0m00.03s
0m00.11s | categories/Structure/Utf8                                          | 0m00.11s || +0m00.00s
0m00.10s | categories/Adjoint/Utf8                                            | 0m00.16s || -0m00.06s
0m00.10s | categories/Profunctor/Core                                         | 0m00.13s || -0m00.03s
0m00.10s | categories/Category/Dual                                           | 0m00.17s || -0m00.07s
0m00.10s | categories/Profunctor/Notations                                    | 0m00.11s || -0m00.00s
0m00.10s | coq/Init/Peano                                                     | 0m00.13s || -0m00.03s
0m00.10s | categories/Functor/Core                                            | 0m00.10s || +0m00.00s
0m00.10s | categories/Category/Subcategory/Wide                               | 0m00.08s || +0m00.02s
0m00.10s | Pointed                                                            | 0m00.08s || +0m00.02s
0m00.10s | categories/ExponentialLaws/Law2/Law2                               | 0m00.13s || -0m00.03s
0m00.10s | categories/Functor/Pointwise/Pointwise                             | 0m00.09s || +0m00.01s
0m00.09s | categories/GroupoidCategory/GroupoidCategory                       | 0m00.11s || -0m00.02s
0m00.09s | categories/Category/Utf8                                           | 0m00.11s || -0m00.02s
0m00.09s | categories/Functor/Identity                                        | 0m00.07s || +0m00.01s
0m00.09s | types/UniverseLevel                                                | 0m00.07s || +0m00.01s
0m00.09s | categories/Category/Core                                           | 0m00.14s || -0m00.05s
0m00.09s | categories/Category/Notations                                      | 0m00.11s || -0m00.02s
0m00.09s | categories/Category/Subcategory/Full                               | 0m00.10s || -0m00.01s
0m00.08s | categories/Category/Strict                                         | 0m00.08s || +0m00.00s
0m00.08s | coq/Init/Specif                                                    | 0m00.07s || +0m00.00s
0m00.08s | categories/SetCategory/Core                                        | 0m00.14s || -0m00.06s
0m00.08s | categories/ExponentialLaws/Law4/Law4                               | 0m00.10s || -0m00.02s
0m00.08s | categories/Category/Subcategory/Subcategory                        | 0m00.16s || -0m00.08s
0m00.08s | hit/TwoSphere                                                      | 0m00.11s || -0m00.03s
0m00.08s | categories/NaturalTransformation/Composition/Composition           | 0m00.11s || -0m00.03s
0m00.08s | types/Empty                                                        | 0m00.11s || -0m00.03s
0m00.07s | categories/Functor/Composition/Core                                | 0m00.11s || -0m00.03s
0m00.07s | UnivalenceAxiom                                                    | 0m00.10s || -0m00.03s
0m00.07s | coq/Program/Tactics                                                | 0m00.06s || +0m00.01s
0m00.06s | coq/Init/Datatypes                                                 | 0m00.07s || -0m00.01s
0m00.06s | coq/Init/Logic_Type                                                | 0m00.06s || +0m00.00s
0m00.06s | FunextAxiom                                                        | 0m00.07s || -0m00.01s
0m00.04s | coq/Init/Notations                                                 | 0m00.04s || +0m00.00s
0m00.04s | coq/Init/Logic                                                     | 0m00.05s || -0m00.01s
0m00.03s | coq/Init/Prelude                                                   | 0m00.04s || -0m00.01s
0m00.03s | coq/Bool/Bool                                                      | 0m00.03s || +0m00.00s
0m00.02s | coq/Init/Tactics                                                   | 0m00.03s || -0m00.00s
Clean up transport_path_forall_hammer

Using the new tactics in terms is cleaner than messing with evars.

After    | File Name                                                          | Before   || Change
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2m55.48s | Total                                                              | 2m49.19s || +0m06.29s
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0m29.01s | categories/Comma/ProjectionFunctors                                | 0m21.36s || +0m07.65s
0m10.19s | categories/ExponentialLaws/Law4/Functors                           | 0m10.54s || -0m00.34s
0m09.52s | categories/Adjoint/Dual                                            | 0m09.85s || -0m00.33s
0m07.61s | categories/Adjoint/Composition/AssociativityLaw                    | 0m07.86s || -0m00.25s
0m07.43s | categories/FunctorCategory/Dual                                    | 0m08.16s || -0m00.73s
0m06.66s | categories/Adjoint/UnitCounit                                      | 0m06.72s || -0m00.05s
0m06.36s | categories/Comma/InducedFunctors                                   | 0m06.75s || -0m00.38s
0m05.35s | categories/Pseudofunctor/RewriteLaws                               | 0m05.45s || -0m00.10s
0m04.83s | categories/Grothendieck/PseudofunctorToCat                         | 0m05.22s || -0m00.38s
0m04.55s | categories/Adjoint/UnitCounitCoercions                             | 0m04.10s || +0m00.45s
0m04.42s | categories/Adjoint/HomCoercions                                    | 0m04.45s || -0m00.03s
0m03.72s | categories/UniversalProperties                                     | 0m03.67s || +0m00.05s
0m03.36s | categories/Pseudofunctor/Identity                                  | 0m03.36s || +0m00.00s
0m03.23s | categories/GroupoidCategory/Morphisms                              | 0m03.00s || +0m00.23s
0m03.04s | categories/Category/Morphisms                                      | 0m03.10s || -0m00.06s
0m02.88s | categories/Adjoint/Composition/IdentityLaws                        | 0m02.79s || +0m00.08s
0m02.85s | categories/Structure/IdentityPrinciple                             | 0m02.83s || +0m00.02s
0m02.74s | categories/Adjoint/Composition/Core                                | 0m02.52s || +0m00.22s
0m02.73s | categories/Comma/Dual                                              | 0m02.77s || -0m00.04s
0m02.60s | categories/Yoneda                                                  | 0m02.42s || +0m00.18s
0m02.44s | categories/Adjoint/UniversalMorphisms                              | 0m02.58s || -0m00.14s
0m02.19s | categories/Functor/Pointwise/Properties                            | 0m02.16s || +0m00.02s
0m02.15s | categories/Pseudofunctor/FromFunctor                               | 0m02.34s || -0m00.18s
0m01.88s | categories/Category/Sigma/OnMorphisms                              | 0m01.82s || +0m00.05s
0m01.86s | categories/ExponentialLaws/Law1/Law                                | 0m01.72s || +0m00.14s
0m01.69s | categories/Functor/Prod/Universal                                  | 0m01.57s || +0m00.11s
0m01.58s | categories/Functor/Attributes                                      | 0m01.55s || +0m00.03s
0m01.57s | categories/Functor/Sum                                             | 0m01.49s || +0m00.08s
0m01.50s | categories/ProductLaws                                             | 0m01.48s || +0m00.02s
0m01.45s | categories/Functor/Paths                                           | 0m01.37s || +0m00.07s
0m01.16s | categories/ExponentialLaws/Law2/Functors                           | 0m01.12s || +0m00.03s
0m01.14s | categories/DualFunctor                                             | 0m01.11s || +0m00.02s
0m01.00s | categories/Adjoint/Paths                                           | 0m01.06s || -0m00.06s
0m00.96s | categories/Limits/Core                                             | 0m00.98s || -0m00.02s
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0m00.91s | categories/PseudonaturalTransformation/Core                        | 0m00.83s || +0m00.08s
0m00.90s | categories/FunctorCategory/Functorial                              | 0m00.70s || +0m00.20s
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0m00.83s | categories/Functor/Composition/Functorial/Core                     | 0m00.99s || -0m00.16s
0m00.81s | categories/Functor/Prod                                            | 0m00.78s || +0m00.03s
0m00.80s | categories/ExponentialLaws/Law0                                    | 0m00.80s || +0m00.00s
0m00.78s | categories/Comma/Core                                              | 0m00.81s || -0m00.03s
0m00.74s | categories/InitialTerminalCategory/Pseudofunctors                  | 0m00.70s || +0m00.04s
0m00.73s | categories/NaturalTransformation/Prod                              | 0m00.73s || +0m00.00s
0m00.72s | categories/HomFunctor                                              | 0m00.79s || -0m00.07s
0m00.62s | categories/Category/Sigma/OnObjects                                | 0m00.58s || +0m00.04s
0m00.62s | categories/Functor/Pointwise                                       | 0m00.61s || +0m00.01s
0m00.57s | categories/ExponentialLaws/Law1/Functors                           | 0m00.59s || -0m00.02s
0m00.54s | categories/NaturalTransformation/Pointwise                         | 0m00.54s || +0m00.00s
0m00.54s | categories/NaturalTransformation/Dual                              | 0m00.62s || -0m00.07s
0m00.53s | categories/Pseudofunctor/Core                                      | 0m00.52s || +0m00.01s
0m00.52s | categories/FunctorCategory/Morphisms                               | 0m00.59s || -0m00.06s
0m00.48s | contrib/HoTTBookExercises                                          | 0m00.51s || -0m00.03s
0m00.45s | categories/SetCategory/Morphisms                                   | 0m00.43s || +0m00.02s
0m00.42s | contrib/HoTTBook                                                   | 0m00.36s || +0m00.06s
0m00.40s | categories/Limits/Functors                                         | 0m00.44s || -0m00.03s
0m00.39s | categories/CategoryOfSections/Core                                 | 0m00.33s || +0m00.06s
0m00.34s | categories/categories                                              | 0m00.36s || -0m00.01s
0m00.33s | categories/Comma/Projection                                        | 0m00.34s || -0m00.01s
0m00.31s | categories/ExponentialLaws/Law3/Functors                           | 0m00.28s || +0m00.02s
0m00.30s | categories/Functor/Composition/Laws                                | 0m00.26s || +0m00.03s
0m00.30s | categories/KanExtensions/Functors                                  | 0m00.32s || -0m00.02s
0m00.29s | Tactics                                                            | 0m00.28s || +0m00.00s
0m00.29s | categories/FundamentalPreGroupoidCategory                          | 0m00.30s || -0m00.01s
0m00.28s | categories/KanExtensions/Core                                      | 0m00.25s || +0m00.03s
0m00.27s | categories/InitialTerminalCategory/Functors                        | 0m00.28s || -0m00.01s
0m00.24s | categories/IndiscreteCategory                                      | 0m00.25s || -0m00.01s
0m00.24s | categories/Adjoint/Adjoint                                         | 0m00.20s || +0m00.03s
0m00.24s | categories/Grothendieck/ToCat                                      | 0m00.26s || -0m00.02s
0m00.23s | categories/NaturalTransformation/Sum                               | 0m00.26s || -0m00.03s
0m00.21s | categories/Cat/Core                                                | 0m00.24s || -0m00.03s
0m00.21s | categories/NaturalTransformation/Composition/Functorial            | 0m00.23s || -0m00.02s
0m00.20s | categories/Functor/Functor                                         | 0m00.20s || +0m00.00s
0m00.20s | categories/Functor/Dual                                            | 0m00.20s || +0m00.00s
0m00.19s | categories/InitialTerminalCategory/NaturalTransformations          | 0m00.20s || -0m00.01s
0m00.18s | categories/ExponentialLaws/ExponentialLaws                         | 0m00.14s || +0m00.03s
0m00.18s | categories/NatCategory                                             | 0m00.20s || -0m00.02s
0m00.18s | categories/HomotopyPreCategory                                     | 0m00.21s || -0m00.03s
0m00.18s | categories/Cat/Morphisms                                           | 0m00.17s || +0m00.00s
0m00.18s | categories/Grothendieck/Grothendieck                               | 0m00.19s || -0m00.01s
0m00.18s | categories/Adjoint/Hom                                             | 0m00.22s || -0m00.04s
0m00.17s | categories/FunctorCategory/Core                                    | 0m00.12s || +0m00.05s
0m00.16s | categories/GroupoidCategory/Core                                   | 0m00.17s || -0m00.01s
0m00.16s | categories/Category/Objects                                        | 0m00.17s || -0m00.01s
0m00.16s | categories/Utf8                                                    | 0m00.16s || +0m00.00s
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0m00.16s | categories/Structure/Structure                                     | 0m00.11s || +0m00.05s
0m00.16s | categories/Functor/Composition/Composition                         | 0m00.18s || -0m00.01s
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0m00.16s | categories/Adjoint/Composition/LawsTactic                          | 0m00.16s || +0m00.00s
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0m00.14s | categories/Limits/Limits                                           | 0m00.12s || +0m00.02s
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0m00.14s | HoTT                                                               | 0m00.11s || +0m00.03s
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0m00.13s | categories/Adjoint/Utf8                                            | 0m00.09s || +0m00.04s
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0m00.10s | categories/ExponentialLaws/Law2/Law2                               | 0m00.12s || -0m00.01s
0m00.10s | categories/Category/Sigma/Sigma                                    | 0m00.11s || -0m00.00s
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Add two more kinds of duals

The identifiers L and R refer to which ^op is removed/inverted.
Functorialize yoneda

Alas, I still don't really understand the Yoneda lemma.

Also, the proof is very long.  I'd be happy if anyone could clean it up.

After    | File Name                          | Before   || Change
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0m08.45s | Total                              | 0m07.85s || +0m00.59s
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0m04.29s | categories/Adjoint/HomCoercions    | 0m04.00s || +0m00.29s
0m02.39s | categories/Yoneda                  | 0m02.28s || +0m00.11s
0m00.64s | categories/SetCategory/Morphisms   | 0m00.43s || +0m00.21s
0m00.43s | categories/categories              | 0m00.40s || +0m00.02s
0m00.41s | contrib/HoTTBook                   | 0m00.47s || -0m00.06s
0m00.18s | categories/Adjoint/Adjoint         | 0m00.18s || +0m00.00s
0m00.12s | categories/SetCategory/SetCategory | 0m00.10s || +0m00.01s
Merge pull request #421 from JasonGross/finished-but-slow-yoneda-unified

Functorialize the yoneda lemma

LGTM
Merge pull request #416 from JasonGross/finished-but-slow-comma-functorial

It's amazing to see category theory done without diagrams.
Merge pull request #418 from JasonGross/clean-transport-path-forall

Clean up transport_path_forall_hammer
WIP