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?

After    | File Name                                                | Before
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8m57.97s | Total                                                    | 8m33.74s
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1m45.72s | categories/Comma/ProjectionFunctors                      | 1m45.60s
0m32.69s | categories/Adjoint/Composition/AssociativityLaw          | 0m33.41s
0m24.70s | categories/Grothendieck/PseudofunctorToCat               | 0m25.47s
0m23.68s | categories/Adjoint/HomCoercions                          |   N/A
0m16.75s | categories/Adjoint/UnitCounitCoercions                   | 0m16.96s
0m16.70s | categories/ExponentialLaws/Law4/Functors                 | 0m17.55s
0m16.14s | categories/Comma/InducedFunctors                         | 0m15.69s
0m15.17s | categories/FunctorCategory/Dual                          | 0m15.70s
0m13.65s | hit/Flattening                                           | 0m12.76s
0m12.29s | categories/Adjoint/Composition/Core                      | 0m12.04s
0m12.08s | categories/Pseudofunctor/Core                            | 0m11.98s
0m12.04s | categories/Functor/Pointwise/Properties                  | 0m12.47s
0m11.92s | categories/Adjoint/Dual                                  | 0m11.75s
0m10.49s | categories/Adjoint/Composition/IdentityLaws              | 0m10.61s
0m10.40s | categories/Pseudofunctor/FromFunctor                     | 0m10.91s
0m08.64s | categories/Yoneda                                        | 0m08.23s
0m08.18s | categories/ExponentialLaws/Law1/Law                      | 0m08.12s
0m08.13s | categories/Functor/Prod/Universal                        | 0m07.82s
0m08.13s | categories/GroupoidCategory/Morphisms                    | 0m07.66s
0m07.10s | hit/Connectedness                                        | 0m07.02s
0m06.90s | categories/UniversalProperties                           | 0m06.76s
0m06.89s | categories/Adjoint/Paths                                 | 0m06.63s
0m06.58s | categories/Structure/IdentityPrinciple                   | 0m06.69s
0m06.24s | categories/Comma/Dual                                    | 0m06.33s
0m06.02s | categories/Functor/Paths                                 | 0m05.63s
0m05.83s | categories/Category/Morphisms                            | 0m05.60s
0m05.74s | categories/Functor/Sum                                   | 0m05.75s
0m05.59s | categories/Adjoint/UnitCounit                            | 0m05.46s
0m05.08s | categories/ExponentialLaws/Law2/Functors                 | 0m04.75s
0m05.04s | EquivalenceVarieties                                     | 0m05.34s
0m04.68s | categories/Category/Sigma/OnMorphisms                    | 0m04.42s
0m04.42s | categories/DualFunctor                                   | 0m04.52s
0m03.66s | categories/ProductLaws                                   | 0m03.59s
0m03.54s | categories/Structure/Core                                | 0m03.57s
0m03.48s | types/ObjectClassifier                                   | 0m03.70s
0m02.99s | types/Sigma                                              | 0m03.16s
0m02.84s | categories/Functor/Prod/Functorial                       | 0m02.88s
0m02.74s | categories/Adjoint/UniversalMorphisms                    | 0m02.85s
0m02.59s | categories/FunctorCategory/Functorial                    | 0m02.65s
0m02.54s | Equivalences                                             | 0m02.50s
0m02.50s | categories/Grothendieck/ToSet                            | 0m02.47s
0m02.23s | categories/Category/Sum                                  | 0m02.24s
0m02.22s | categories/Functor/Attributes                            | 0m02.22s
0m02.06s | categories/Category/Sigma/Core                           | 0m02.06s
0m02.03s | PathGroupoids                                            | 0m01.76s
0m02.00s | categories/Comma/Core                                    | 0m01.94s
0m01.89s | categories/NaturalTransformation/Isomorphisms            | 0m01.92s
0m01.84s | categories/HomFunctor                                    | 0m01.73s
0m01.78s | categories/NaturalTransformation/Dual                    | 0m01.86s
0m01.66s | categories/FunctorCategory/Morphisms                     | 0m01.68s
0m01.59s | categories/NaturalTransformation/Paths                   | 0m01.69s
0m01.40s | categories/NaturalTransformation/Pointwise               | 0m01.46s
0m01.30s | categories/Category/Prod                                 | 0m01.26s
0m01.28s | categories/Category/Sigma/OnObjects                      | 0m01.44s
0m01.26s | categories/NaturalTransformation/Composition/Laws        | 0m01.23s
0m01.22s | types/Prod                                               | 0m01.29s
0m01.16s | categories/Limits/Core                                   | 0m01.09s
0m01.10s | hit/Spheres                                              | 0m00.87s
0m01.08s | categories/Functor/Pointwise                             | 0m01.04s
0m01.02s | categories/CategoryOfSections/Core                       | 0m01.04s
0m01.02s | categories/ExponentialLaws/Law1/Functors                 | 0m01.03s
0m00.96s | hit/epi                                                  | 0m00.89s
0m00.96s | categories/ExponentialLaws/Law  N/A                      | 0m00.98s
0m00.93s | categories/Functor/Prod                                  | 0m00.92s
0m00.91s | types/Paths                                              | 0m00.87s
0m00.91s | contrib/HoTTBookExercises                                | 0m00.84s
0m00.90s | categories/NaturalTransformation/Prod                    | 0m00.89s
0m00.85s | categories/Functor/Composition/Functorial                | 0m00.85s
0m00.74s | Trunc                                                    | 0m00.77s
0m00.68s | categories/InitialTerminalCategory                       | 0m00.65s
0m00.64s | types/Sum                                                | 0m00.56s
0m00.64s | categories/NaturalTransformation/Composition/Core        | 0m00.64s
0m00.62s | types/Universe                                           | 0m00.65s
0m00.57s | contrib/HoTTBook                                         | 0m00.62s
0m00.57s | hit/quotient                                             | 0m00.54s
0m00.56s | categories/NaturalTransformation/Sum                     | 0m00.52s
0m00.56s | categories/categories                                    | 0m00.57s
0m00.54s | types/Record                                             | 0m00.53s
0m00.53s | Functorish                                               | 0m00.54s
0m00.53s | hit/Suspension                                           | 0m00.69s
0m00.52s | categories/Functor/Composition/Laws                      | 0m00.45s
0m00.50s | categories/Limits/Functors                               | 0m00.47s
0m00.49s | categories/Comma/Projection                              | 0m00.53s
0m00.47s | HProp                                                    | 0m00.52s
0m00.46s | hit/Circle                                               | 0m00.57s
0m00.46s | categories/KanExtensions/Functors                        | 0m00.45s
0m00.45s | types/Forall                                             | 0m00.45s
0m00.44s | categories/ExponentialLaws/Law3/Functors                 | 0m00.44s
0m00.43s | HSet                                                     | 0m00.48s
0m00.43s | Tactics                                                  | 0m00.42s
0m00.42s | categories/NaturalTransformation/Identity                | 0m00.38s
0m00.39s | categories/Cat/Core                                      | 0m00.41s
0m00.37s | categories/Functor/Dual                                  | 0m00.38s
0m00.37s | categories/Functor/Functor                               | 0m00.33s
0m00.37s | Fibrations                                               | 0m00.40s
0m00.36s | TruncType                                                | 0m00.36s
0m00.32s | categories/IndiscreteCategory                            | 0m00.35s
0m00.31s | categories/Cat/Morphisms                                 | 0m00.32s
0m00.30s | hit/minus1Trunc                                          | 0m00.26s
0m00.30s | categories/NaturalTransformation/Composition/Functorial  | 0m00.30s
0m00.29s | categories/ExponentialLaws/ExponentialLaws               | 0m00.26s
0m00.29s | Misc                                                     | 0m00.36s
0m00.28s | categories/KanExtensions/Core                            | 0m00.30s
0m00.26s | categories/Adjoint/Hom                                   |   N/A
0m00.26s | categories/Functor/Composition/Core                      | 0m00.22s
0m00.26s | types/Arrow                                              | 0m00.27s
0m00.26s | categories/Grothendieck/Grothendieck                     | 0m00.29s
0m00.24s | categories/Utf8                                          | 0m00.20s
0m00.24s | categories/Notations                                     | 0m00.21s
0m00.24s | categories/Adjoint/Adjoint                               | 0m00.21s
0m00.22s | hit/iso                                                  | 0m00.20s
0m00.22s | categories/SetCategory/Functors/Functors                 | 0m00.18s
0m00.22s | categories/Comma/Comma                                   | 0m00.17s
0m00.22s | categories/Category/Objects                              | 0m00.25s
0m00.21s | categories/FunctorCategory/FunctorCategory               | 0m00.15s
0m00.21s | categories/Pseudofunctor/Pseudofunctor                   | 0m00.19s
0m00.20s | Conjugation                                              | 0m00.21s
0m00.20s | categories/NaturalTransformation/NaturalTransformation   | 0m00.21s
0m00.20s | FunextVarieties                                          | 0m00.15s
0m00.20s | types/Bool                                               | 0m00.17s
0m00.19s | categories/Cat/Cat                                       | 0m00.17s
0m00.19s | categories/Functor/Prod/Prod                             | 0m00.14s
0m00.18s | categories/DependentProduct                              | 0m00.18s
0m00.18s | categories/Grothendieck/ToCat                            | 0m00.19s
0m00.18s | categories/NatCategory                                   | 0m00.20s
0m00.18s | categories/FunctorCategory/Core                          | 0m00.18s
0m00.17s | categories/Adjoint/Utf8                                  | 0m00.14s
0m00.17s | categories/Limits/Limits                                 | 0m00.16s
0m00.17s | categories/Category/Category                             | 0m00.19s
0m00.17s | categories/Adjoint/Composition/Composition               | 0m00.18s
0m00.16s | categories/KanExtensions/KanExtensions                   | 0m00.16s
0m00.16s | HoTT                                                     | 0m00.15s
0m00.16s | categories/Profunctor/Notations                          | 0m00.12s
0m00.16s | categories/Functor/Notations                             | 0m00.16s
0m00.16s | categories/GroupoidCategory/Core                         | 0m00.19s
0m00.16s | categories/Functor/Utf8                                  | 0m00.13s
0m00.16s | hit/TwoSphere                                            | 0m00.12s
0m00.16s | categories/ExponentialLaws/Law1/Law1                     | 0m00.14s
0m00.16s | categories/ExponentialLaws/Law2/Law2                     | 0m00.17s
0m00.15s | categories/Profunctor/Core                               | 0m00.14s
0m00.15s | categories/Adjoint/Notations                             | 0m00.17s
0m00.15s | categories/NaturalTransformation/Core                    | 0m00.15s
0m00.15s | categories/NaturalTransformation/Notations               | 0m00.14s
0m00.15s | categories/NaturalTransformation/Utf8                    | 0m00.14s
0m00.15s | Overture                                                 | 0m00.17s
0m00.14s | categories/Adjoint/Identity                              | 0m00.14s
0m00.14s | categories/Profunctor/Identity                           | 0m00.13s
0m00.14s | categories/Adjoint/Composition/LawsTactic                | 0m00.12s
0m00.14s | categories/CategoryOfSections/CategoryOfSections         | 0m00.14s
0m00.13s | categories/DiscreteCategory                              | 0m00.11s
0m00.13s | hit/Interval                                             | 0m00.11s
0m00.13s | categories/SetCategory/Core                              | 0m00.12s
0m00.13s | categories/Category/Dual                                 | 0m00.15s
0m00.13s | categories/Profunctor/Representable                      | 0m00.17s
0m00.13s | categories/Category/Core                                 | 0m00.14s
0m00.13s | categories/Category/Sigma/Sigma                          | 0m00.14s
0m00.13s | categories/Profunctor/Utf8                               | 0m00.17s
0m00.12s | categories/Comma/Utf8                                    | 0m00.15s
0m00.12s | categories/ExponentialLaws/Law3/Law3                     | 0m00.13s
0m00.12s | Contractible                                             | 0m00.11s
0m00.12s | categories/ExponentialLaws/Law4/Law4                     | 0m00.11s
0m00.12s | categories/Category/Univalent                            | 0m00.12s
0m00.12s | categories/Profunctor/Profunctor                         | 0m00.14s
0m00.12s | categories/Comma/Notations                               | 0m00.13s
0m00.12s | categories/SetCategory/SetCategory                       | 0m00.10s
0m00.12s | UnivalenceAxiom                                          | 0m00.11s
0m00.12s | categories/NaturalTransformation/Composition/Composition | 0m00.11s
0m00.12s | categories/Category/Subcategory/Full                     | 0m00.12s
0m00.12s | categories/Functor/Pointwise/Pointwise                   | 0m00.08s
0m00.12s | categories/FunctorCategory/Notations                     | 0m00.12s
0m00.12s | hit/Truncations                                          | 0m00.12s
0m00.11s | categories/Adjoint/Core                                  | 0m00.11s
0m00.11s | categories/GroupoidCategory/GroupoidCategory             | 0m00.10s
0m00.11s | categories/Category/Utf8                                 | 0m00.12s
0m00.11s | categories/Structure/Structure                           | 0m00.17s
0m00.11s | coq/Init/Peano                                           | 0m00.11s
0m00.11s | hit/unique_choice                                        | 0m00.15s
0m00.11s | types/Unit                                               | 0m00.12s
0m00.11s | categories/Functor/Composition/Composition               | 0m00.13s
0m00.10s | categories/Functor/Identity                              | 0m00.07s
0m00.10s | categories/FunctorCategory/Utf8                          | 0m00.16s
0m00.10s | categories/Functor/Core                                  | 0m00.12s
0m00.10s | categories/Category/Subcategory/Wide                     | 0m00.10s
0m00.10s | categories/Category/Notations                            | 0m00.10s
0m00.09s | categories/Structure/Notations                           | 0m00.10s
0m00.09s | categories/Category/Subcategory/Subcategory              | 0m00.11s
0m00.09s | Pointed                                                  | 0m00.08s
0m00.09s | categories/Structure/Utf8                                | 0m00.11s
0m00.08s | categories/Category/Strict                               | 0m00.08s
0m00.08s | types/UniverseLevel                                      | 0m00.08s
0m00.08s | types/Empty                                              | 0m00.07s
0m00.07s | coq/Init/Datatypes                                       | 0m00.06s
0m00.06s | coq/Init/Notations                                       | 0m00.04s
0m00.06s | coq/Init/Specif                                          | 0m00.07s
0m00.06s | coq/Init/Logic_Type                                      | 0m00.06s
0m00.06s | FunextAxiom                                              | 0m00.05s
0m00.05s | coq/Program/Tactics                                      | 0m00.06s
0m00.04s | coq/Bool/Bool                                            | 0m00.02s
0m00.03s | coq/Init/Logic                                           | 0m00.03s
0m00.03s | coq/Init/Prelude                                         | 0m00.02s
0m00.03s | coq/Init/Tactics                                         | 0m00.03s