Update some typeclasses and add discrete category

After    | File Name                             | Before
-----------------------------------------------------------
1m48.24s | PreCategory/Equality                  | 1m40.46s
0m18.10s | Functor/Equality                      | 0m13.74s
0m10.87s | NaturalTransformation/Equality        | 0m06.93s
0m02.36s | ProductPreCategory                    | 0m01.84s
0m02.17s | Functor/CompositionLaws               | 0m02.13s
0m02.08s | NaturalTransformation/Composition     | 0m02.13s
0m01.95s | SumPreCategory                        | 0m01.89s
0m01.47s | NaturalTransformation/CompositionLaws | 0m01.40s
0m00.27s | NaturalTransformation/Identity        | 0m00.26s
0m00.24s | FunctorPreCategory                    | 0m00.22s
0m00.24s | Common                                | 0m00.26s
0m00.23s | Functor/Composition                   | 0m00.23s
0m00.14s | PreCategory/Core                      | 0m00.15s
0m00.14s | Functor/Core                          | 0m00.12s
0m00.14s | NaturalTransformation/Core            | 0m00.14s
0m00.12s | DiscretePreCategory                   |   N/A
0m00.09s | NaturalTransformation                 | 0m00.07s
0m00.09s | Functor/Identity                      | 0m00.08s
0m00.09s | StrictCategory                        | 0m00.08s
0m00.08s | Utf8                                  | 0m00.07s
0m00.08s | Functor                               | 0m00.11s
0m00.06s | PreCategory                           | 0m00.10s
0m00.04s | NotationsUtf8                         | 0m00.04s
0m00.04s | Notations                             | 0m00.04s
-----------------------------------------------------------
2m29.32s | Total                                 | 2m12.49s
Fix an instance, add some proofs about Bool
Add BoolCat

After    | File Name                             | Before
-----------------------------------------------------------
1m45.00s | PreCategory/Equality                  | 1m40.14s
0m18.28s | Functor/Equality                      | 0m17.80s
0m10.57s | NaturalTransformation/Equality        | 0m09.97s
0m02.27s | ProductPreCategory                    | 0m02.27s
0m02.18s | NaturalTransformation/Composition     | 0m02.24s
0m02.15s | Functor/CompositionLaws               | 0m02.14s
0m01.94s | SumPreCategory                        | 0m01.84s
0m01.34s | NaturalTransformation/CompositionLaws | 0m01.41s
0m00.25s | NaturalTransformation/Identity        | 0m00.29s
0m00.24s | FunctorPreCategory                    | 0m00.24s
0m00.24s | Functor/Composition                   | 0m00.24s
0m00.20s | Common                                | 0m00.20s
0m00.14s | PreCategory/Core                      | 0m00.16s
0m00.12s | DiscretePreCategory                   | 0m00.11s
0m00.11s | NaturalTransformation                 | 0m00.09s
0m00.10s | Functor/Core                          | 0m00.10s
0m00.09s | NaturalTransformation/Core            | 0m00.09s
0m00.08s | Functor/Identity                      | 0m00.08s
0m00.08s | StrictCategory                        | 0m00.06s
0m00.08s | PreCategory                           | 0m00.06s
0m00.06s | Utf8                                  | 0m00.07s
0m00.06s | Functor                               | 0m00.08s
0m00.06s | Notations                             | 0m00.04s
0m00.05s | NotationsUtf8                         | 0m00.05s
-----------------------------------------------------------
2m25.68s | Total                                 | 2m19.77s
Add BoolCat to Makefile
Add Coq.Init.Peano
Modify Peano to work with HoTT

After    | File Name                             | Before
-----------------------------------------------------------
1m46.16s | PreCategory/Equality                  | 1m46.45s
0m17.80s | Functor/Equality                      | 0m18.21s
0m09.94s | NaturalTransformation/Equality        | 0m10.08s
0m02.30s | ProductPreCategory                    | 0m02.33s
0m02.20s | NaturalTransformation/Composition     | 0m02.24s
0m02.06s | Functor/CompositionLaws               | 0m02.08s
0m01.72s | SumPreCategory                        | 0m01.85s
0m01.34s | NaturalTransformation/CompositionLaws | 0m01.36s
0m00.57s | BoolCategory                          | 0m00.59s
0m00.23s | NaturalTransformation/Identity        | 0m00.28s
0m00.23s | FunctorPreCategory                    | 0m00.26s
0m00.23s | Functor/Composition                   | 0m00.26s
0m00.22s | Common                                | 0m00.23s
0m00.16s | PreCategory/Core                      | 0m00.15s
0m00.14s | Functor/Core                          | 0m00.11s
0m00.13s | NaturalTransformation/Core            | 0m00.12s
0m00.12s | Peano                                 |   N/A
0m00.11s | DiscretePreCategory                   | 0m00.11s
0m00.09s | NaturalTransformation                 | 0m00.08s
0m00.08s | StrictCategory                        | 0m00.09s
0m00.07s | Utf8                                  | 0m00.06s
0m00.06s | Functor/Identity                      | 0m00.09s
0m00.06s | PreCategory                           | 0m00.10s
0m00.05s | NotationsUtf8                         | 0m00.05s
0m00.05s | Functor                               | 0m00.08s
0m00.04s | Notations                             | 0m00.05s
-----------------------------------------------------------
2m26.15s | Total                                 | 2m27.31s
Update HoTT
Fix up some notations and tactics
Add epi, mono, and iso

After    | File Name                             | Before
-----------------------------------------------------------
1m40.35s | PreCategory/Equality                  | 1m41.82s
0m17.85s | Functor/Equality                      | 0m17.13s
0m10.20s | NaturalTransformation/Equality        | 0m10.24s
0m06.79s | PreCategoryMorphisms                  |   N/A
0m02.20s | Functor/CompositionLaws               | 0m02.05s
0m02.16s | ProductPreCategory                    | 0m02.12s
0m02.11s | NaturalTransformation/Composition     | 0m02.15s
0m01.74s | SumPreCategory                        | 0m01.78s
0m01.39s | NaturalTransformation/CompositionLaws | 0m01.44s
0m00.53s | BoolCategory                          | 0m00.56s
0m00.24s | Functor/Composition                   | 0m00.22s
0m00.23s | NaturalTransformation/Identity        | 0m00.25s
0m00.22s | Common                                | 0m00.21s
0m00.21s | FunctorPreCategory                    | 0m00.22s
0m00.14s | PreCategory/Core                      | 0m00.16s
0m00.14s | NaturalTransformation/Core            | 0m00.13s
0m00.10s | Functor/Core                          | 0m00.10s
0m00.10s | DiscretePreCategory                   | 0m00.12s
0m00.10s | Peano                                 | 0m00.14s
0m00.09s | Functor/Identity                      | 0m00.08s
0m00.09s | StrictCategory                        | 0m00.08s
0m00.08s | NaturalTransformation                 | 0m00.08s
0m00.07s | Utf8                                  | 0m00.06s
0m00.07s | PreCategory                           | 0m00.06s
0m00.07s | Functor                               | 0m00.08s
0m00.04s | NotationsUtf8                         | 0m00.05s
0m00.04s | Notations                             | 0m00.06s
-----------------------------------------------------------
2m27.34s | Total                                 | 2m21.38s
Add Category.v

After    | File Name                             | Before
-----------------------------------------------------------
1m45.65s | PreCategory/Equality                  | 1m42.97s
0m17.93s | Functor/Equality                      | 0m17.36s
0m10.34s | NaturalTransformation/Equality        | 0m10.30s
0m06.83s | PreCategoryMorphisms                  | 0m07.07s
0m02.30s | NaturalTransformation/Composition     | 0m02.26s
0m02.26s | ProductPreCategory                    | 0m02.24s
0m02.19s | Functor/CompositionLaws               | 0m02.16s
0m01.85s | SumPreCategory                        | 0m01.74s
0m01.42s | NaturalTransformation/CompositionLaws | 0m01.42s
0m00.55s | BoolCategory                          | 0m00.61s
0m00.26s | Common                                | 0m00.19s
0m00.25s | NaturalTransformation/Identity        | 0m00.26s
0m00.24s | Functor/Composition                   | 0m00.20s
0m00.21s | FunctorPreCategory                    | 0m00.20s
0m00.16s | PreCategory/Core                      | 0m00.18s
0m00.14s | DiscretePreCategory                   | 0m00.14s
0m00.12s | NaturalTransformation/Core            | 0m00.12s
0m00.11s | Functor/Core                          | 0m00.13s
0m00.10s | NaturalTransformation                 | 0m00.10s
0m00.09s | Category                              |   N/A
0m00.09s | Peano                                 | 0m00.11s
0m00.08s | StrictCategory                        | 0m00.10s
0m00.08s | Functor                               | 0m00.08s
0m00.07s | Functor/Identity                      | 0m00.08s
0m00.07s | PreCategory                           | 0m00.08s
0m00.06s | Utf8                                  | 0m00.06s
0m00.05s | NotationsUtf8                         | 0m00.03s
0m00.03s | Notations                             | 0m00.04s
-----------------------------------------------------------
2m33.53s | Total                                 | 2m30.22s