Fix Book.py to work with Python 2.6

This involves minor changes in re, and inserting a workaround using
optparse if argparse is unavailable.
Handle \texorpdfstring in labels
Merge pull request #349 from JasonGross/etc-book-py-26

Fix Book.py to work with Python 2.6
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
------------------------------------------------------------------------------
8m57.97s | Total                                                    | 8m33.74s
------------------------------------------------------------------------------
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
Factor the hom set equivalence into a part not needing funext

This is so we can use it to show that adjunctions preserve
initial/terminal objects (and, more generally, universal morphisms,
kan extensions, (co)limits, etc).

After    | File Name                                                | Before
------------------------------------------------------------------------------
9m02.84s | Total                                                    | 9m01.12s
------------------------------------------------------------------------------
1m47.29s | categories/Comma/ProjectionFunctors                      | 1m45.84s
0m34.52s | categories/Adjoint/Composition/AssociativityLaw          | 0m34.33s
0m25.27s | categories/Grothendieck/PseudofunctorToCat               | 0m23.94s
0m21.09s | categories/Adjoint/HomCoercions                          | 0m23.62s
0m17.52s | categories/ExponentialLaws/Law4/Functors                 | 0m16.57s
0m16.34s | categories/Comma/InducedFunctors                         | 0m16.17s
0m15.94s | categories/Adjoint/UnitCounitCoercions                   | 0m16.50s
0m15.68s | categories/FunctorCategory/Dual                          | 0m16.51s
0m12.77s | hit/Flattening                                           | 0m13.29s
0m12.60s | categories/Pseudofunctor/Core                            | 0m11.91s
0m12.20s | categories/Adjoint/Composition/Core                      | 0m11.84s
0m12.00s | categories/Functor/Pointwise/Properties                  | 0m12.80s
0m11.50s | categories/Adjoint/Dual                                  | 0m11.12s
0m10.97s | categories/Pseudofunctor/FromFunctor                     | 0m10.53s
0m10.59s | categories/Adjoint/Composition/IdentityLaws              | 0m10.52s
0m08.46s | categories/Functor/Prod/Universal                        | 0m07.94s
0m08.43s | categories/Yoneda                                        | 0m08.02s
0m08.26s | categories/GroupoidCategory/Morphisms                    | 0m08.28s
0m08.04s | categories/ExponentialLaws/Law1/Law                      | 0m08.47s
0m07.06s | hit/Connectedness                                        | 0m07.08s
0m06.93s | categories/UniversalProperties                           | 0m06.98s
0m06.67s | categories/Comma/Dual                                    | 0m06.64s
0m06.59s | categories/Adjoint/Paths                                 | 0m06.25s
0m06.55s | categories/Structure/IdentityPrinciple                   | 0m06.60s
0m06.26s | categories/Adjoint/UnitCounit                            | 0m06.05s
0m06.10s | categories/Category/Morphisms                            | 0m05.90s
0m05.96s | categories/Functor/Paths                                 | 0m06.11s
0m05.68s | categories/Functor/Sum                                   | 0m05.91s
0m05.40s | EquivalenceVarieties                                     | 0m05.39s
0m04.93s | categories/ExponentialLaws/Law2/Functors                 | 0m04.64s
0m04.58s | categories/DualFunctor                                   | 0m05.28s
0m04.57s | categories/Category/Sigma/OnMorphisms                    | 0m04.43s
0m03.87s | categories/ProductLaws                                   | 0m03.69s
0m03.56s | categories/Structure/Core                                | 0m03.53s
0m03.49s | types/ObjectClassifier                                   | 0m03.39s
0m03.12s | types/Sigma                                              | 0m03.03s
0m03.05s | categories/Functor/Prod/Functorial                       | 0m02.78s
0m02.76s | categories/Adjoint/UniversalMorphisms                    | 0m02.78s
0m02.59s | categories/Comma/Core                                    | 0m02.01s
0m02.58s | categories/FunctorCategory/Functorial                    | 0m02.95s
0m02.54s | categories/Grothendieck/ToSet                            | 0m02.79s
0m02.44s | Equivalences                                             | 0m02.48s
0m02.24s | categories/Category/Sum                                  | 0m02.21s
0m02.15s | categories/Functor/Attributes                            | 0m02.21s
0m01.95s | categories/Category/Sigma/Core                           | 0m01.89s
0m01.92s | categories/NaturalTransformation/Dual                    | 0m01.82s
0m01.89s | PathGroupoids                                            | 0m01.93s
0m01.89s | categories/NaturalTransformation/Isomorphisms            | 0m01.89s
0m01.78s | categories/HomFunctor                                    | 0m01.87s
0m01.75s | categories/FunctorCategory/Morphisms                     | 0m01.62s
0m01.68s | categories/NaturalTransformation/Paths                   | 0m01.65s
0m01.38s | categories/NaturalTransformation/Pointwise               | 0m01.42s
0m01.37s | categories/Category/Sigma/OnObjects                      | 0m01.22s
0m01.30s | categories/NaturalTransformation/Composition/Laws        | 0m01.22s
0m01.26s | categories/Category/Prod                                 | 0m01.26s
0m01.26s | categories/NaturalTransformation/Prod                    | 0m00.97s
0m01.23s | types/Prod                                               | 0m01.31s
0m01.18s | categories/ExponentialLaws/Law1/Functors                 | 0m01.06s
0m01.17s | categories/Limits/Core                                   | 0m01.13s
0m01.12s | categories/ExponentialLaws/Law  N/A                      | 0m01.03s
0m01.04s | categories/Functor/Pointwise                             | 0m01.09s
0m01.01s | categories/CategoryOfSections/Core                       | 0m01.01s
0m00.91s | hit/epi                                                  | 0m00.92s
0m00.91s | hit/Spheres                                              | 0m01.00s
0m00.89s | categories/Functor/Prod                                  | 0m00.96s
0m00.89s | contrib/HoTTBookExercises                                | 0m00.93s
0m00.86s | categories/Functor/Composition/Functorial                | 0m00.90s
0m00.86s | types/Paths                                              | 0m00.87s
0m00.79s | Trunc                                                    | 0m00.77s
0m00.71s | contrib/HoTTBook                                         | 0m00.63s
0m00.68s | categories/InitialTerminalCategory                       | 0m00.64s
0m00.67s | types/Universe                                           | 0m00.69s
0m00.63s | categories/NaturalTransformation/Composition/Core        | 0m00.60s
0m00.58s | types/Sum                                                | 0m00.61s
0m00.57s | Functorish                                               | 0m00.56s
0m00.55s | categories/SetCategory/Morphisms                         | 0m00.59s
0m00.55s | categories/categories                                    | 0m00.56s
0m00.55s | hit/quotient                                             | 0m00.54s
0m00.53s | HProp                                                    | 0m00.51s
0m00.52s | categories/NaturalTransformation/Sum                     | 0m00.52s
0m00.52s | categories/Comma/Projection                              | 0m00.58s
0m00.50s | hit/Suspension                                           | 0m00.56s
0m00.49s | types/Record                                             | 0m00.48s
0m00.49s | hit/Circle                                               | 0m00.54s
0m00.48s | categories/Limits/Functors                               | 0m00.42s
0m00.46s | categories/Cat/Core                                      | 0m00.47s
0m00.46s | HSet                                                     | 0m00.47s
0m00.45s | categories/ExponentialLaws/Law3/Functors                 | 0m00.43s
0m00.45s | Tactics                                                  | 0m00.50s
0m00.45s | categories/Functor/Composition/Laws                      | 0m00.55s
0m00.40s | categories/KanExtensions/Functors                        | 0m00.44s
0m00.38s | categories/Functor/Dual                                  | 0m00.28s
0m00.38s | categories/NaturalTransformation/Identity                | 0m00.42s
0m00.38s | types/Forall                                             | 0m00.44s
0m00.34s | TruncType                                                | 0m00.36s
0m00.32s | categories/Functor/Functor                               | 0m00.36s
0m00.32s | Fibrations                                               | 0m00.38s
0m00.32s | categories/KanExtensions/Core                            | 0m00.24s
0m00.31s | categories/IndiscreteCategory                            | 0m00.31s
0m00.31s | Misc                                                     | 0m00.26s
0m00.30s | categories/Adjoint/Hom                                   | 0m00.29s
0m00.28s | hit/minus1Trunc                                          | 0m00.26s
0m00.27s | types/Arrow                                              | 0m00.25s
0m00.27s | categories/Cat/Morphisms                                 | 0m00.30s
0m00.26s | categories/ExponentialLaws/ExponentialLaws               | 0m00.27s
0m00.26s | categories/Category/Objects                              | 0m00.23s
0m00.26s | categories/Adjoint/Adjoint                               | 0m00.24s
0m00.26s | categories/Grothendieck/Grothendieck                     | 0m00.30s
0m00.24s | categories/NaturalTransformation/Composition/Functorial  | 0m00.30s
0m00.23s | categories/NaturalTransformation/NaturalTransformation   | 0m00.19s
0m00.23s | categories/Functor/Composition/Core                      | 0m00.25s
0m00.23s | categories/Notations                                     | 0m00.20s
0m00.22s | Conjugation                                              | 0m00.16s
0m00.22s | categories/Grothendieck/ToCat                            | 0m00.19s
0m00.22s | categories/Utf8                                          | 0m00.25s
0m00.21s | categories/Functor/Prod/Prod                             | 0m00.18s
0m00.20s | categories/FunctorCategory/FunctorCategory               | 0m00.18s
0m00.20s | categories/FunctorCategory/Core                          | 0m00.19s
0m00.19s | categories/SetCategory/Functors/Functors                 | 0m00.22s
0m00.19s | categories/Comma/Comma                                   | 0m00.20s
0m00.18s | categories/DependentProduct                              | 0m00.20s
0m00.18s | categories/Cat/Cat                                       | 0m00.19s
0m00.18s | hit/iso                                                  | 0m00.22s
0m00.18s | categories/Category/Category                             | 0m00.17s
0m00.18s | categories/Category/Core                                 | 0m00.14s
0m00.18s | FunextVarieties                                          | 0m00.21s
0m00.18s | types/Bool                                               | 0m00.19s
0m00.17s | categories/Limits/Limits                                 | 0m00.14s
0m00.17s | categories/SetCategory/Core                              | 0m00.12s
0m00.17s | categories/Adjoint/Notations                             | 0m00.14s
0m00.17s | categories/NatCategory                                   | 0m00.17s
0m00.17s | categories/Adjoint/Composition/Composition               | 0m00.13s
0m00.17s | categories/Functor/Utf8                                  | 0m00.18s
0m00.17s | categories/NaturalTransformation/Notations               | 0m00.19s
0m00.17s | Overture                                                 | 0m00.18s
0m00.16s | categories/Comma/Utf8                                    | 0m00.15s
0m00.16s | HoTT                                                     | 0m00.21s
0m00.16s | categories/GroupoidCategory/Core                         | 0m00.16s
0m00.16s | categories/NaturalTransformation/Core                    | 0m00.14s
0m00.16s | categories/Profunctor/Representable                      | 0m00.15s
0m00.16s | categories/Adjoint/Composition/LawsTactic                | 0m00.14s
0m00.15s | categories/Adjoint/Utf8                                  | 0m00.15s
0m00.15s | categories/KanExtensions/KanExtensions                   | 0m00.12s
0m00.15s | categories/FunctorCategory/Utf8                          | 0m00.13s
0m00.15s | categories/Adjoint/Identity                              | 0m00.15s
0m00.15s | categories/Pseudofunctor/Pseudofunctor                   | 0m00.22s
0m00.15s | categories/ExponentialLaws/Law1/Law1                     | 0m00.13s
0m00.14s | categories/ExponentialLaws/Law3/Law3                     | 0m00.17s
0m00.14s | categories/Adjoint/Core                                  | 0m00.11s
0m00.14s | categories/Profunctor/Core                               | 0m00.15s
0m00.14s | categories/Category/Dual                                 | 0m00.19s
0m00.14s | categories/Profunctor/Notations                          | 0m00.12s
0m00.14s | categories/Functor/Notations                             | 0m00.17s
0m00.14s | categories/Comma/Notations                               | 0m00.14s
0m00.14s | categories/SetCategory/SetCategory                       | 0m00.10s
0m00.14s | types/Unit                                               | 0m00.13s
0m00.13s | categories/Functor/Core                                  | 0m00.09s
0m00.13s | hit/TwoSphere                                            | 0m00.13s
0m00.13s | categories/Profunctor/Identity                           | 0m00.13s
0m00.13s | hit/Truncations                                          | 0m00.14s
0m00.12s | categories/Category/Utf8                                 | 0m00.12s
0m00.12s | coq/Init/Peano                                           | 0m00.12s
0m00.12s | hit/unique_choice                                        | 0m00.15s
0m00.12s | categories/Profunctor/Profunctor                         | 0m00.13s
0m00.12s | categories/ExponentialLaws/Law2/Law2                     | 0m00.17s
0m00.12s | categories/Profunctor/Utf8                               | 0m00.11s
0m00.11s | hit/Interval                                             | 0m00.13s
0m00.11s | categories/Structure/Structure                           | 0m00.12s
0m00.11s | categories/Category/Notations                            | 0m00.12s
0m00.11s | categories/NaturalTransformation/Composition/Composition | 0m00.13s
0m00.11s | categories/Functor/Pointwise/Pointwise                   | 0m00.12s
0m00.11s | categories/NaturalTransformation/Utf8                    | 0m00.17s
0m00.11s | categories/FunctorCategory/Notations                     | 0m00.14s
0m00.11s | categories/CategoryOfSections/CategoryOfSections         | 0m00.14s
0m00.10s | categories/DiscreteCategory                              | 0m00.12s
0m00.10s | categories/GroupoidCategory/GroupoidCategory             | 0m00.12s
0m00.10s | Contractible                                             | 0m00.09s
0m00.10s | categories/Category/Univalent                            | 0m00.12s
0m00.10s | categories/Category/Subcategory/Wide                     | 0m00.10s
0m00.10s | categories/Category/Subcategory/Subcategory              | 0m00.12s
0m00.10s | categories/Category/Sigma/Sigma                          | 0m00.15s
0m00.10s | categories/Functor/Composition/Composition               | 0m00.15s
0m00.10s | categories/Category/Subcategory/Full                     | 0m00.14s
0m00.09s | categories/Structure/Utf8                                | 0m00.12s
0m00.08s | categories/Category/Strict                               | 0m00.10s
0m00.08s | categories/ExponentialLaws/Law4/Law4                     | 0m00.10s
0m00.08s | types/UniverseLevel                                      | 0m00.07s
0m00.08s | UnivalenceAxiom                                          | 0m00.11s
0m00.07s | categories/Functor/Identity                              | 0m00.09s
0m00.07s | coq/Init/Specif                                          | 0m00.06s
0m00.07s | categories/Structure/Notations                           | 0m00.12s
0m00.07s | Pointed                                                  | 0m00.10s
0m00.06s | coq/Init/Logic_Type                                      | 0m00.06s
0m00.06s | coq/Program/Tactics                                      | 0m00.06s
0m00.06s | FunextAxiom                                              | 0m00.06s
0m00.06s | types/Empty                                              | 0m00.06s
0m00.04s | coq/Init/Notations                                       | 0m00.03s
0m00.04s | coq/Init/Datatypes                                       | 0m00.08s
0m00.04s | coq/Init/Logic                                           | 0m00.03s
0m00.04s | coq/Bool/Bool                                            | 0m00.02s
0m00.04s | coq/Init/Tactics                                         | 0m00.03s
0m00.03s | coq/Init/Prelude                                         | 0m00.02s
Merge pull request #356 from JasonGross/adjoint-hom

Hom-set adjunctions
Add many entries to categories TOC

Hopefully the TOC can now be a decent entry point for categories
Merge pull request #360 from JasonGross/document-categories

Add many entries to categories TOC
Connect Lemma 9.1.8
Add some more category theory from the book
Merge pull request #363 from JasonGross/cat-book

Add some more category theory from the book
Prove [IsEquiv (ap pr1)] for [HProp] and [HSet]

This is useful for proving that the precategory of sets is a category.

After    | File Name                                                | Before
------------------------------------------------------------------------------
0m03.18s | HSet                                                     | 0m00.47s
0m02.77s | HProp                                                    | 0m00.93s
------------------------------------------------------------------------------
9m14.97s | Total                                                    | 9m16.12s
------------------------------------------------------------------------------
1m45.63s | categories/Comma/ProjectionFunctors                      | 1m47.41s
0m35.09s | categories/Adjoint/Composition/AssociativityLaw          | 0m35.10s
0m25.74s | categories/Grothendieck/PseudofunctorToCat               | 0m25.78s
0m21.15s | categories/Adjoint/HomCoercions                          | 0m22.18s
0m17.47s | categories/ExponentialLaws/Law4/Functors                 | 0m17.50s
0m17.38s | categories/Adjoint/UnitCounitCoercions                   | 0m17.58s
0m16.12s | categories/FunctorCategory/Dual                          | 0m16.53s
0m16.06s | categories/Comma/InducedFunctors                         | 0m16.43s
0m13.79s | hit/Flattening                                           | 0m13.99s
0m12.64s | categories/Adjoint/Dual                                  | 0m11.92s
0m12.54s | categories/Functor/Pointwise/Properties                  | 0m12.56s
0m12.50s | categories/Adjoint/Composition/Core                      | 0m12.89s
0m12.42s | categories/Pseudofunctor/Core                            | 0m12.01s
0m11.16s | categories/Pseudofunctor/FromFunctor                     | 0m11.00s
0m11.10s | categories/Adjoint/Composition/IdentityLaws              | 0m10.70s
0m08.28s | categories/ExponentialLaws/Law1/Law                      | 0m08.00s
0m08.24s | categories/Functor/Prod/Universal                        | 0m08.08s
0m08.11s | categories/Yoneda                                        | 0m08.77s
0m08.06s | categories/GroupoidCategory/Morphisms                    | 0m08.52s
0m07.58s | hit/Connectedness                                        | 0m06.82s
0m06.98s | categories/UniversalProperties                           | 0m07.56s
0m06.96s | categories/Structure/IdentityPrinciple                   | 0m07.12s
0m06.42s | categories/Adjoint/Paths                                 | 0m06.76s
0m06.33s | categories/Comma/Dual                                    | 0m06.88s
0m06.30s | categories/Adjoint/UnitCounit                            | 0m05.91s
0m06.28s | categories/Category/Morphisms                            | 0m05.94s
0m06.14s | categories/Functor/Paths                                 | 0m06.20s
0m05.78s | categories/Functor/Sum                                   | 0m06.08s
0m05.58s | EquivalenceVarieties                                     | 0m05.74s
0m05.05s | categories/ExponentialLaws/Law2/Functors                 | 0m05.16s
0m04.94s | categories/DualFunctor                                   | 0m04.63s
0m04.60s | categories/Category/Sigma/OnMorphisms                    | 0m04.47s
0m03.78s | categories/ProductLaws                                   | 0m03.86s
0m03.68s | categories/Structure/Core                                | 0m03.59s
0m03.32s | types/ObjectClassifier                                   | 0m04.01s
0m03.26s | types/Sigma                                              | 0m03.28s
0m03.18s | HSet                                                     | 0m00.47s
0m03.01s | categories/FunctorCategory/Functorial                    | 0m02.84s
0m02.77s | HProp                                                    | 0m00.93s
0m02.76s | categories/Functor/Prod/Functorial                       | 0m02.95s
0m02.75s | Equivalences                                             | 0m02.51s
0m02.75s | categories/Adjoint/UniversalMorphisms                    | 0m02.97s
0m02.43s | categories/Grothendieck/ToSet                            | 0m02.55s
0m02.30s | categories/Functor/Attributes                            | 0m02.28s
0m02.25s | categories/Category/Sum                                  | 0m02.13s
0m02.18s | categories/Comma/Core                                    | 0m02.34s
0m02.03s | categories/Category/Sigma/Core                           | 0m02.08s
0m02.02s | PathGroupoids                                            | 0m01.92s
0m01.95s | categories/NaturalTransformation/Isomorphisms            | 0m02.02s
0m01.87s | categories/HomFunctor                                    | 0m01.82s
0m01.82s | categories/NaturalTransformation/Dual                    | 0m01.90s
0m01.71s | categories/NaturalTransformation/Paths                   | 0m01.68s
0m01.67s | categories/FunctorCategory/Morphisms                     | 0m01.85s
0m01.43s | categories/Category/Sigma/OnObjects                      | 0m01.34s
0m01.31s | categories/NaturalTransformation/Pointwise               | 0m01.38s
0m01.31s | categories/Category/Prod                                 | 0m01.27s
0m01.30s | types/Prod                                               | 0m01.27s
0m01.19s | categories/NaturalTransformation/Composition/Laws        | 0m01.28s
0m01.06s | categories/ExponentialLaws/Law1/Functors                 | 0m01.07s
0m01.04s | categories/Functor/Pointwise                             | 0m01.15s
0m01.04s | categories/CategoryOfSections/Core                       | 0m01.09s
0m01.01s | hit/epi                                                  | 0m00.87s
0m01.01s | categories/Limits/Core                                   | 0m01.11s
0m01.00s | categories/ExponentialLaws/Law  N/A                      | 0m01.01s
0m01.00s | categories/NaturalTransformation/Prod                    | 0m01.02s
0m00.96s | categories/Functor/Prod                                  | 0m00.92s
0m00.96s | contrib/HoTTBookExercises                                | 0m01.05s
0m00.94s | hit/Spheres                                              | 0m00.96s
0m00.88s | types/Paths                                              | 0m00.98s
0m00.84s | categories/Functor/Composition/Functorial                | 0m00.92s
0m00.72s | contrib/HoTTBook                                         | 0m00.72s
0m00.68s | categories/InitialTerminalCategory                       | 0m00.61s
0m00.65s | Trunc                                                    | 0m00.78s
0m00.64s | types/Sum                                                | 0m00.61s
0m00.64s | categories/NaturalTransformation/Composition/Core        | 0m00.63s
0m00.63s | categories/categories                                    | 0m00.53s
0m00.61s | Functorish                                               | 0m00.53s
0m00.60s | types/Universe                                           | 0m00.63s
0m00.60s | hit/quotient                                             | 0m00.56s
0m00.58s | categories/SetCategory/Morphisms                         | 0m00.51s
0m00.55s | categories/NaturalTransformation/Sum                     | 0m00.60s
0m00.52s | types/Record                                             | 0m00.49s
0m00.52s | categories/Functor/Composition/Laws                      | 0m00.50s
0m00.52s | categories/Comma/Projection                              | 0m00.58s
0m00.51s | hit/Suspension                                           | 0m00.62s
0m00.48s | categories/Limits/Functors                               | 0m00.46s
0m00.48s | hit/Circle                                               | 0m00.76s
0m00.44s | categories/NaturalTransformation/Identity                | 0m00.40s
0m00.44s | categories/KanExtensions/Functors                        | 0m00.43s
0m00.43s | Tactics                                                  | 0m00.44s
0m00.39s | categories/Functor/Functor                               | 0m00.44s
0m00.38s | categories/ExponentialLaws/Law3/Functors                 | 0m00.44s
0m00.37s | categories/IndiscreteCategory                            | 0m00.28s
0m00.37s | types/Forall                                             | 0m00.45s
0m00.36s | categories/FundamentalPreGroupoidCategory                | 0m00.34s
0m00.36s | categories/Functor/Dual                                  | 0m00.37s
0m00.36s | Fibrations                                               | 0m00.36s
0m00.35s | categories/Cat/Core                                      | 0m00.42s
0m00.34s | TruncType                                                | 0m00.38s
0m00.33s | categories/Cat/Morphisms                                 | 0m00.31s
0m00.32s | categories/KanExtensions/Core                            | 0m00.32s
0m00.31s | categories/HomotopyPreCategory                           | 0m00.35s
0m00.30s | categories/Grothendieck/Grothendieck                     | 0m00.26s
0m00.29s | types/Arrow                                              | 0m00.30s
0m00.28s | Misc                                                     | 0m00.30s
0m00.27s | categories/ExponentialLaws/ExponentialLaws               | 0m00.24s
0m00.27s | categories/Adjoint/Hom                                   | 0m00.29s
0m00.27s | categories/NaturalTransformation/Composition/Functorial  | 0m00.35s
0m00.26s | hit/minus1Trunc                                          | 0m00.24s
0m00.25s | categories/Adjoint/Adjoint                               | 0m00.23s
0m00.23s | categories/NaturalTransformation/NaturalTransformation   | 0m00.16s
0m00.23s | categories/FunctorCategory/FunctorCategory               | 0m00.20s
0m00.23s | categories/Utf8                                          | 0m00.21s
0m00.23s | FunextVarieties                                          | 0m00.21s
0m00.22s | categories/Category/Objects                              | 0m00.26s
0m00.22s | categories/Functor/Composition/Core                      | 0m00.23s
0m00.22s | categories/Notations                                     | 0m00.22s
0m00.21s | categories/DependentProduct                              | 0m00.25s
0m00.21s | categories/Grothendieck/ToCat                            | 0m00.22s
0m00.21s | types/Bool                                               | 0m00.23s
0m00.20s | categories/Comma/Comma                                   | 0m00.21s
0m00.20s | categories/NatCategory                                   | 0m00.18s
0m00.20s | categories/NaturalTransformation/Notations               | 0m00.14s
0m00.19s | hit/iso                                                  | 0m00.19s
0m00.19s | categories/Pseudofunctor/Pseudofunctor                   | 0m00.19s
0m00.18s | categories/Profunctor/Representable                      | 0m00.11s
0m00.18s | Modality                                                 | 0m00.19s
0m00.18s | categories/Category/Category                             | 0m00.16s
0m00.18s | categories/NaturalTransformation/Core                    | 0m00.17s
0m00.18s | categories/ExponentialLaws/Law2/Law2                     | 0m00.18s
0m00.17s | Conjugation                                              | 0m00.18s
0m00.17s | categories/ExponentialLaws/Law3/Law3                     | 0m00.15s
0m00.17s | categories/FunctorCategory/Utf8                          | 0m00.19s
0m00.17s | categories/Functor/Prod/Prod                             | 0m00.20s
0m00.17s | categories/Category/Univalent                            | 0m00.12s
0m00.17s | categories/Functor/Composition/Composition               | 0m00.14s
0m00.17s | categories/NaturalTransformation/Utf8                    | 0m00.15s
0m00.17s | Overture                                                 | 0m00.15s
0m00.17s | categories/FunctorCategory/Core                          | 0m00.13s
0m00.16s | categories/Adjoint/Utf8                                  | 0m00.17s
0m00.16s | categories/Limits/Limits                                 | 0m00.14s
0m00.16s | categories/Cat/Cat                                       | 0m00.17s
0m00.16s | categories/SetCategory/Functors/Functors                 | 0m00.23s
0m00.16s | categories/SetCategory/Core                              | 0m00.16s
0m00.16s | HoTT                                                     | 0m00.17s
0m00.16s | categories/Category/Dual                                 | 0m00.15s
0m00.16s | categories/Adjoint/Identity                              | 0m00.14s
0m00.16s | categories/Comma/Notations                               | 0m00.18s
0m00.16s | categories/Adjoint/Composition/Composition               | 0m00.16s
0m00.16s | hit/TwoSphere                                            | 0m00.16s
0m00.16s | categories/FunctorCategory/Notations                     | 0m00.14s
0m00.15s | categories/Adjoint/Notations                             | 0m00.17s
0m00.15s | categories/Functor/Utf8                                  | 0m00.19s
0m00.15s | categories/Category/Subcategory/Subcategory              | 0m00.10s
0m00.15s | categories/Category/Core                                 | 0m00.15s
0m00.14s | categories/Comma/Utf8                                    | 0m00.16s
0m00.14s | categories/DiscreteCategory                              | 0m00.12s
0m00.14s | categories/Category/Utf8                                 | 0m00.10s
0m00.14s | categories/KanExtensions/KanExtensions                   | 0m00.14s
0m00.14s | categories/Profunctor/Core                               | 0m00.14s
0m00.14s | categories/Profunctor/Notations                          | 0m00.12s
0m00.14s | types/Unit                                               | 0m00.13s
0m00.14s | hit/Truncations                                          | 0m00.14s
0m00.14s | categories/Profunctor/Utf8                               | 0m00.12s
0m00.13s | categories/ExponentialLaws/Law4/Law4                     | 0m00.09s
0m00.13s | categories/GroupoidCategory/Core                         | 0m00.16s
0m00.13s | categories/SetCategory/SetCategory                       | 0m00.11s
0m00.13s | categories/ExponentialLaws/Law1/Law1                     | 0m00.20s
0m00.12s | categories/Structure/Structure                           | 0m00.12s
0m00.12s | categories/Functor/Core                                  | 0m00.09s
0m00.12s | categories/Functor/Notations                             | 0m00.17s
0m00.12s | categories/Category/Subcategory/Wide                     | 0m00.11s
0m00.12s | categories/Category/Notations                            | 0m00.11s
0m00.12s | UnivalenceAxiom                                          | 0m00.13s
0m00.12s | categories/Functor/Pointwise/Pointwise                   | 0m00.15s
0m00.12s | categories/Adjoint/Composition/LawsTactic                | 0m00.14s
0m00.12s | categories/CategoryOfSections/CategoryOfSections         | 0m00.14s
0m00.11s | hit/Interval                                             | 0m00.15s
0m00.11s | hit/unique_choice                                        | 0m00.13s
0m00.11s | categories/Profunctor/Profunctor                         | 0m00.14s
0m00.11s | categories/NaturalTransformation/Composition/Composition | 0m00.12s
0m00.10s | categories/Adjoint/Core                                  | 0m00.11s
0m00.10s | coq/Init/Peano                                           | 0m00.09s
0m00.10s | categories/Structure/Notations                           | 0m00.10s
0m00.10s | Pointed                                                  | 0m00.12s
0m00.10s | categories/Category/Subcategory/Full                     | 0m00.12s
0m00.10s | categories/Structure/Utf8                                | 0m00.11s
0m00.10s | types/Empty                                              | 0m00.07s
0m00.09s | categories/GroupoidCategory/GroupoidCategory             | 0m00.11s
0m00.09s | categories/Profunctor/Identity                           | 0m00.14s
0m00.08s | Contractible                                             | 0m00.08s
0m00.08s | categories/Category/Sigma/Sigma                          | 0m00.15s
0m00.07s | categories/Functor/Identity                              | 0m00.08s
0m00.07s | categories/Category/Strict                               | 0m00.09s
0m00.06s | coq/Init/Datatypes                                       | 0m00.06s
0m00.06s | types/UniverseLevel                                      | 0m00.06s
0m00.06s | coq/Init/Logic_Type                                      | 0m00.05s
0m00.05s | coq/Init/Specif                                          | 0m00.06s
0m00.05s | coq/Program/Tactics                                      | 0m00.05s
0m00.05s | FunextAxiom                                              | 0m00.05s
0m00.04s | coq/Init/Prelude                                         | 0m00.01s
0m00.04s | coq/Bool/Bool                                            | 0m00.02s
0m00.04s | coq/Init/Tactics                                         | 0m00.04s
0m00.02s | coq/Init/Notations                                       | 0m00.04s
0m00.02s | coq/Init/Logic                                           | 0m00.04s
Merge pull request #361 from JasonGross/isequiv-ap-setT

Prove that [ap pr1] is an equivalence for [HProp] and [HSet]
Fixups to work with the latest polyproj branch.
Progress on adapting HoTT and categories to latest polyproj branch.
Progress on adapting HoTT and categories to latest polyproj branch.
Adapt categories and hit's code to latest polyproj (Private keyword).
- A few places raise universe inconsistencies in Categories still, not sure why.
- Some minor unification problems with apply/eauto discovered as well.
- Some places requiring more instances of Funext, as I expected.
Everything compiles quickly here.
Update submodule
Fix up some transparency issues
Remove an admit