HoTT/HoTT — pull request #251 by JasonGross (2013-11-16 08:42:57+00:00)
Title: Port some basic adjoints from HoTT-categories

Next up, connecting adjoints and universal morphisms. This might have a bit more automation than most of the other pull requests I've made, though hopefully nothing is automated to the point of it being confusing.

```
After | File Name | Before
------------------------------------------------------------------------------
4m36.98s | Total | 3m55.29s
------------------------------------------------------------------------------
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
```