Port some basic adjoints from HoTT-categories

After    | File Name                                                | Before
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4m36.98s | Total                                                    | 3m55.29s
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0m28.54s | categories/Comma/Dual                                    | 0m27.37s
0m17.26s | categories/ExponentialLaws/Law4/Functors                 | 0m16.86s
0m16.50s | categories/Functor/Paths                                 | 0m16.02s
0m16.11s | categories/Adjoint/UnitCounitCoercions                   |   N/A
0m12.68s | hit/Flattening                                           | 0m13.51s
0m11.70s | categories/Adjoint/Dual                                  |   N/A
0m10.74s | categories/Comma/InducedFunctors                         | 0m10.26s
0m10.23s | categories/Functor/Pointwise/Properties                  | 0m09.97s
0m08.34s | categories/Functor/Prod/Universal                        | 0m08.04s
0m08.02s | categories/ExponentialLaws/Law1/Law                      | 0m08.52s
0m07.77s | categories/GroupoidCategory/Morphisms                    | 0m07.97s
0m07.47s | hit/Connectedness                                        | 0m07.49s
0m07.40s | categories/UniversalProperties                           | 0m07.84s
0m06.66s | categories/Adjoint/Paths                                 |   N/A
0m05.86s | categories/Adjoint/UnitCounit                            |   N/A
0m05.80s | categories/Functor/Sum                                   | 0m05.95s
0m05.64s | categories/Category/Morphisms                            | 0m05.61s
0m05.00s | categories/ExponentialLaws/Law2/Functors                 | 0m05.01s
0m04.86s | EquivalenceVarieties                                     | 0m05.02s
0m04.36s | categories/Category/Sigma/OnMorphisms                    | 0m04.20s
0m03.92s | categories/ProductLaws                                   | 0m03.71s
0m03.58s | types/ObjectClassifier                                   | 0m03.98s
0m02.91s | categories/Functor/Prod/Functorial                       | 0m02.98s
0m02.86s | types/Sigma                                              | 0m02.86s
0m02.82s | categories/FunctorCategory/Functorial                    | 0m02.60s
0m02.58s | Equivalences                                             | 0m02.65s
0m02.28s | categories/Functor/Attributes                            | 0m02.62s
0m02.20s | categories/Category/Sum                                  | 0m02.25s
0m02.04s | categories/Category/Sigma/Core                           | 0m02.04s
0m01.97s | categories/NaturalTransformation/Dual                    | 0m02.07s
0m01.94s | PathGroupoids                                            | 0m01.90s
0m01.80s | categories/HomFunctor                                    | 0m01.78s
0m01.69s | categories/FunctorCategory/Morphisms                     | 0m01.62s
0m01.68s | categories/NaturalTransformation/Composition/Laws        | 0m01.66s
0m01.67s | categories/NaturalTransformation/Paths                   | 0m01.68s
0m01.54s | categories/Comma/Core                                    | 0m01.59s
0m01.45s | categories/Category/Sigma/OnObjects                      | 0m01.42s
0m01.34s | categories/NaturalTransformation/Composition/Core        | 0m01.31s
0m01.30s | categories/Category/Prod                                 | 0m01.32s
0m01.27s | types/Prod                                               | 0m01.28s
0m01.24s | categories/NaturalTransformation/Composition/Functorial  | 0m01.14s
0m01.10s | categories/Limits/Limits                                 | 0m01.05s
0m01.07s | categories/Functor/Pointwise                             | 0m01.05s
0m00.98s | categories/ExponentialLaws/Law1/Functors                 | 0m00.96s
0m00.94s | categories/ExponentialLaws/Law  N/A                      | 0m01.00s
0m00.92s | hit/Spheres                                              | 0m00.94s
0m00.92s | categories/NaturalTransformation/Prod                    | 0m00.95s
0m00.90s | categories/Functor/Composition/Functorial                | 0m00.84s
0m00.89s | types/Paths                                              | 0m00.79s
0m00.86s | categories/Functor/Prod                                  | 0m01.07s
0m00.83s | hit/epi                                                  | 0m00.93s
0m00.81s | Trunc                                                    | 0m00.80s
0m00.72s | categories/KanExtensions/KanExtensions                   | 0m00.60s
0m00.68s | types/Sum                                                | 0m00.64s
0m00.61s | types/Universe                                           | 0m00.59s
0m00.59s | categories/InitialTerminalCategory                       | 0m00.66s
0m00.55s | categories/NaturalTransformation/Sum                     | 0m00.53s
0m00.54s | Functorish                                               | 0m00.53s
0m00.54s | categories/Comma/Projection                              | 0m00.53s
0m00.53s | categories/Functor/Composition/Laws                      | 0m00.48s
0m00.52s | hit/quotient                                             | 0m00.54s
0m00.50s | hit/Circle                                               | 0m00.42s
0m00.48s | types/Record                                             | 0m00.50s
0m00.47s | categories/ExponentialLaws/Law3/Functors                 | 0m00.44s
0m00.47s | hit/Suspension                                           | 0m00.47s
0m00.44s | HProp                                                    | 0m00.40s
0m00.41s | HSet                                                     | 0m00.34s
0m00.40s | types/Forall                                             | 0m00.40s
0m00.39s | Tactics                                                  | 0m00.40s
0m00.39s | categories/Cat/Core                                      | 0m00.43s
0m00.38s | categories/categories                                    | 0m00.34s
0m00.35s | Fibrations                                               | 0m00.33s
0m00.30s | categories/IndiscreteCategory                            | 0m00.29s
0m00.30s | categories/Cat/Morphisms                                 | 0m00.26s
0m00.30s | TruncType                                                | 0m00.36s
0m00.28s | categories/Functor/Functor                               | 0m00.30s
0m00.27s | categories/Category/Objects                              | 0m00.24s
0m00.27s | Misc                                                     | 0m00.28s
0m00.26s | categories/ExponentialLaws/ExponentialLaws               | 0m00.26s
0m00.26s | hit/minus1Trunc                                          | 0m00.28s
0m00.26s | categories/NaturalTransformation/Identity                | 0m00.25s
0m00.24s | categories/Functor/Composition/Core                      | 0m00.25s
0m00.24s | categories/Functor/Dual                                  | 0m00.23s
0m00.22s | types/Arrow                                              | 0m00.22s
0m00.19s | categories/SetCategory/Functors/Functors                 | 0m00.19s
0m00.18s | Conjugation                                              | 0m00.18s
0m00.18s | hit/iso                                                  | 0m00.18s
0m00.18s | hit/unique_choice                                        | 0m00.13s
0m00.17s | categories/NatCategory                                   | 0m00.13s
0m00.17s | FunextVarieties                                          | 0m00.18s
0m00.16s | categories/Notations                                     | 0m00.19s
0m00.16s | categories/FunctorCategory/Core                          | 0m00.17s
0m00.15s | categories/Category/Category                             | 0m00.14s
0m00.15s | categories/Functor/Prod/Prod                             | 0m00.16s
0m00.15s | categories/NaturalTransformation/Core                    | 0m00.12s
0m00.15s | categories/Utf8                                          | 0m00.19s
0m00.14s | categories/Comma/Utf8                                    | 0m00.14s
0m00.14s | categories/Functor/Notations                             | 0m00.12s
0m00.14s | categories/SetCategory/Core                              | 0m00.12s
0m00.14s | categories/NaturalTransformation/Notations               | 0m00.14s
0m00.14s | types/Unit                                               | 0m00.13s
0m00.14s | categories/ExponentialLaws/Law2/Law2                     | 0m00.11s
0m00.14s | categories/NaturalTransformation/Utf8                    | 0m00.13s
0m00.14s | Overture                                                 | 0m00.13s
0m00.13s | categories/ExponentialLaws/Law3/Law3                     | 0m00.14s
0m00.13s | categories/Profunctor/Representable                      | 0m00.13s
0m00.13s | categories/Category/Dual                                 | 0m00.13s
0m00.13s | categories/FunctorCategory/FunctorCategory               | 0m00.13s
0m00.12s | categories/Comma/Notations                               | 0m00.10s
0m00.12s | HoTT                                                     | 0m00.09s
0m00.12s | categories/Comma/Comma                                   | 0m00.16s
0m00.12s | hit/Interval                                             | 0m00.10s
0m00.12s | categories/ExponentialLaws/Law4/Law4                     | 0m00.07s
0m00.12s | categories/Profunctor/Notations                          | 0m00.09s
0m00.12s | categories/Functor/Composition/Composition               | 0m00.11s
0m00.11s | categories/GroupoidCategory/Core                         | 0m00.14s
0m00.11s | categories/Category/Core                                 | 0m00.13s
0m00.11s | categories/Cat/Cat                                       | 0m00.15s
0m00.11s | categories/NaturalTransformation/NaturalTransformation   | 0m00.15s
0m00.11s | categories/FunctorCategory/Utf8                          | 0m00.10s
0m00.11s | categories/Functor/Utf8                                  | 0m00.12s
0m00.11s | Contractible                                             | 0m00.10s
0m00.11s | categories/Adjoint/Adjoint                               |   N/A
0m00.11s | types/Bool                                               | 0m00.12s
0m00.11s | categories/Profunctor/Identity                           | 0m00.12s
0m00.11s | categories/ExponentialLaws/Law1/Law1                     | 0m00.12s
0m00.11s | categories/Adjoint/Identity                              |   N/A
0m00.11s | categories/FunctorCategory/Notations                     | 0m00.09s
0m00.11s | categories/Category/Univalent                            | 0m00.12s
0m00.10s | categories/DiscreteCategory                              | 0m00.08s
0m00.10s | categories/GroupoidCategory/GroupoidCategory             | 0m00.09s
0m00.10s | categories/Adjoint/Utf8                                  |   N/A
0m00.10s | categories/Category/Utf8                                 | 0m00.10s
0m00.10s | categories/Profunctor/Core                               | 0m00.12s
0m00.10s | hit/Truncations                                          | 0m00.08s
0m00.10s | categories/Category/Subcategory/Subcategory              | 0m00.10s
0m00.10s | coq/Init/Peano                                           | 0m00.10s
0m00.10s | categories/Functor/Pointwise/Pointwise                   | 0m00.07s
0m00.10s | categories/Profunctor/Utf8                               | 0m00.12s
0m00.10s | categories/Profunctor/Profunctor                         | 0m00.10s
0m00.09s | coq/Init/Specif                                          | 0m00.06s
0m00.09s | categories/Adjoint/Core                                  |   N/A
0m00.09s | categories/NaturalTransformation/Composition/Composition | 0m00.11s
0m00.09s | categories/Category/Sigma/Sigma                          | 0m00.12s
0m00.09s | categories/Adjoint/Notations                             |   N/A
0m00.08s | categories/Category/Subcategory/Wide                     | 0m00.08s
0m00.08s | categories/SetCategory/SetCategory                       | 0m00.10s
0m00.08s | categories/Category/Notations                            | 0m00.10s
0m00.08s | UnivalenceAxiom                                          | 0m00.09s
0m00.08s | categories/Category/Subcategory/Full                     | 0m00.09s
0m00.08s | categories/Functor/Core                                  | 0m00.08s
0m00.07s | categories/Functor/Identity                              | 0m00.05s
0m00.06s | categories/Category/Strict                               | 0m00.03s
0m00.06s | types/Empty                                              | 0m00.08s
0m00.05s | coq/Init/Datatypes                                       | 0m00.04s
0m00.05s | coq/Init/Logic_Type                                      | 0m00.06s
0m00.04s | coq/Init/Notations                                       | 0m00.02s
0m00.04s | coq/Init/Prelude                                         | 0m00.04s
0m00.04s | coq/Init/Tactics                                         | 0m00.04s
0m00.04s | coq/Program/Tactics                                      | 0m00.04s
0m00.04s | FunextAxiom                                              | 0m00.08s
0m00.03s | coq/Init/Logic                                           | 0m00.03s
0m00.02s | coq/Bool/Bool                                            | 0m00.03s