Use modules for reflective subuniverses and modalities
Handle universes carefully to correct module type implementations
improve module comments

After    | File Name                                                 | Before   || Change
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2m44.27s | Total                                                     | 2m43.58s || +0m00.69s
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0m27.96s | hit/V                                                     | 0m16.78s || +0m11.17s
0m07.43s | categories/ExponentialLaws/Law4/Law                       | 0m09.54s || -0m02.10s
0m08.92s | categories/ExponentialLaws/Law3/Law                       | 0m10.14s || -0m01.22s
0m02.59s | contrib/HoTTBook                                          | 0m01.15s || +0m01.43s
0m00.82s | hit/quotient                                              | 0m01.88s || -0m01.06s
0m00.62s | hit/PropositionalFracture                                 | 0m02.20s || -0m01.58s
0m14.18s | contrib/Freudenthal                                       | 0m13.19s || +0m00.99s
0m08.73s | categories/ExponentialLaws/Law2/Law                       | 0m09.63s || -0m00.90s
0m08.65s | Factorization                                             | 0m08.54s || +0m00.11s
0m05.44s | Modality                                                  | 0m05.26s || +0m00.18s
0m04.10s | categories/Comma/ProjectionFunctors                       | 0m05.02s || -0m00.92s
0m03.77s | categories/LaxComma/CoreLaws                              | 0m04.16s || -0m00.39s
0m02.96s | categories/Comma/Functorial                               | 0m02.98s || -0m00.02s
0m02.04s | hit/Flattening                                            | 0m02.06s || -0m00.02s
0m02.02s | hit/Localization                                          | 0m02.08s || -0m00.06s
0m01.98s | Types/Equiv                                               | 0m02.03s || -0m00.04s
0m01.98s | ReflectiveSubuniverse                                     | 0m02.26s || -0m00.27s
0m01.97s | categories/GroupoidCategory/Morphisms                     | 0m01.98s || -0m00.01s
0m01.78s | categories/Adjoint/Composition/AssociativityLaw           | 0m01.83s || -0m00.05s
0m01.59s | categories/ExponentialLaws/Law1/Law                       | 0m01.68s || -0m00.08s
0m01.58s | hit/epi                                                   | 0m01.82s || -0m00.24s
0m01.42s | categories/Category/Morphisms                             | 0m01.42s || +0m00.00s
0m01.30s | categories/ExponentialLaws/Law4/Functors                  | 0m01.55s || -0m00.25s
0m01.26s | contrib/HoTTBookExercises                                 | 0m01.33s || -0m00.07s
0m01.22s | categories/Grothendieck/PseudofunctorToCat                | 0m01.32s || -0m00.10s
0m01.20s | categories/Functor/Paths                                  | 0m01.25s || -0m00.05s
0m01.19s | categories/Functor/Sum                                    | 0m01.21s || -0m00.02s
0m01.14s | categories/Functor/Composition/Laws                       | 0m01.22s || -0m00.08s
0m01.04s | categories/Adjoint/HomCoercions                           | 0m01.12s || -0m00.08s
0m00.98s | categories/Adjoint/Composition/IdentityLaws               | 0m01.10s || -0m00.12s
0m00.98s | Types/Paths                                               | 0m00.98s || +0m00.00s
0m00.92s | categories/UniversalProperties                            | 0m01.00s || -0m00.07s
0m00.92s | categories/Functor/Pointwise/Properties                   | 0m01.05s || -0m00.13s
0m00.91s | Basics/Equivalences                                       | 0m00.88s || +0m00.03s
0m00.90s | categories/Yoneda                                         | 0m00.96s || -0m00.05s
0m00.86s | categories/Pseudofunctor/RewriteLaws                      | 0m00.98s || -0m00.12s
0m00.83s | Basics/PathGroupoids                                      | 0m00.81s || +0m00.01s
0m00.78s | categories/Comma/InducedFunctors                          | 0m00.90s || -0m00.12s
0m00.76s | categories/Pseudofunctor/FromFunctor                      | 0m00.90s || -0m00.14s
0m00.75s | categories/Adjoint/UnitCounitCoercions                    | 0m00.72s || +0m00.03s
0m00.73s | EquivalenceVarieties                                      | 0m00.75s || -0m00.02s
0m00.73s | categories/Pseudofunctor/Identity                         | 0m00.82s || -0m00.08s
0m00.73s | Types/Sigma                                               | 0m00.77s || -0m00.04s
0m00.72s | categories/Category/Sigma/OnMorphisms                     | 0m00.72s || +0m00.00s
0m00.71s | categories/Functor/Composition/Functorial/Attributes      | 0m01.47s || -0m00.76s
0m00.65s | categories/Adjoint/Composition/Core                       | 0m00.66s || -0m00.01s
0m00.62s | categories/Category/Sigma/Core                            | 0m00.65s || -0m00.03s
0m00.58s | Extensions                                                | 0m00.60s || -0m00.02s
0m00.51s | categories/Comma/Core                                     | 0m00.53s || -0m00.02s
0m00.50s | categories/LaxComma/CoreParts                             | 0m00.53s || -0m00.03s
0m00.48s | categories/Structure/IdentityPrinciple                    | 0m00.50s || -0m00.02s
0m00.48s | categories/Comma/Dual                                     | 0m00.47s || +0m00.01s
0m00.46s | categories/Functor/Attributes                             | 0m00.46s || +0m00.00s
0m00.45s | hit/Spheres                                               | 0m00.44s || +0m00.01s
0m00.44s | categories/LaxComma/Core                                  | 0m00.55s || -0m00.11s
0m00.44s | categories/Category/Sum                                   | 0m00.44s || +0m00.00s
0m00.43s | categories/Functor/Prod/Universal                         | 0m00.44s || -0m00.01s
0m00.42s | categories/ProductLaws                                    | 0m00.58s || -0m00.15s
0m00.39s | categories/ExponentialLaws/Law0                           | 0m00.62s || -0m00.23s
0m00.38s | categories/Adjoint/Paths                                  | 0m00.40s || -0m00.02s
0m00.37s | categories/SetCategory/Morphisms                          | 0m00.36s || +0m00.01s
0m00.36s | categories/NaturalTransformation/Paths                    | 0m00.36s || +0m00.00s
0m00.35s | categories/DualFunctor                                    | 0m00.38s || -0m00.03s
0m00.33s | categories/Adjoint/UniversalMorphisms                     | 0m00.29s || +0m00.04s
0m00.33s | categories/InitialTerminalCategory/Pseudofunctors         | 0m00.33s || +0m00.00s
0m00.32s | Types/Universe                                            | 0m00.28s || +0m00.03s
0m00.31s | categories                                                | 0m00.32s || -0m00.01s
0m00.31s | categories/Functor/Composition/Functorial/Core            | 0m00.43s || -0m00.12s
0m00.30s | categories/FundamentalPreGroupoidCategory                 | 0m00.56s || -0m00.26s
0m00.30s | Types/Prod                                                | 0m00.32s || -0m00.02s
0m00.29s | categories/NaturalTransformation/Isomorphisms             | 0m00.39s || -0m00.10s
0m00.28s | hit/Connectedness                                         | 0m00.31s || -0m00.02s
0m00.28s | categories/ExponentialLaws/Law1/Functors                  | 0m00.44s || -0m00.15s
0m00.27s | categories/Limits/Core                                    | 0m00.42s || -0m00.14s
0m00.25s | categories/HomotopyPreCategory                            | 0m00.49s || -0m00.24s
0m00.24s | Types/Sum                                                 | 0m00.20s || +0m00.03s
0m00.24s | TruncType                                                 | 0m00.28s || -0m00.04s
0m00.23s | categories/FunctorCategory/Morphisms                      | 0m00.28s || -0m00.05s
0m00.23s | categories/Functor/Pointwise/Core                         | 0m00.32s || -0m00.09s
0m00.22s | categories/ExponentialLaws/Law2/Functors                  | 0m00.26s || -0m00.04s
0m00.22s | categories/NaturalTransformation/Prod                     | 0m00.22s || +0m00.00s
0m00.22s | ObjectClassifier                                          | 0m00.22s || +0m00.00s
0m00.22s | categories/CategoryOfSections/Core                        | 0m00.19s || +0m00.03s
0m00.22s | hit/Circle                                                | 0m00.22s || +0m00.00s
0m00.22s | hit/Join                                                  | 0m00.21s || +0m00.01s
0m00.22s | hit/Nullification                                         |   N/A    || +0m00.22s
0m00.21s | categories/NaturalTransformation/Composition/Laws         | 0m00.20s || +0m00.00s
0m00.21s | categories/InitialTerminalCategory/Functors               | 0m00.24s || -0m00.03s
0m00.21s | categories/Grothendieck/ToSet                             | 0m00.22s || -0m00.01s
0m00.21s | Fibrations                                                | 0m00.23s || -0m00.02s
0m00.21s | categories/Functor/Prod/Core                              | 0m00.24s || -0m00.03s
0m00.20s | categories/Functor                                        | 0m00.13s || +0m00.07s
0m00.19s | HoTT                                                      | 0m00.12s || +0m00.07s
0m00.19s | categories/Limits/Functors                                | 0m00.30s || -0m00.10s
0m00.18s | hit/Pushout                                               | 0m00.17s || +0m00.00s
0m00.18s | categories/NaturalTransformation/Pointwise                | 0m00.22s || -0m00.04s
0m00.18s | categories/PseudonaturalTransformation/Core               | 0m00.22s || -0m00.04s
0m00.18s | HSet                                                      | 0m00.16s || +0m00.01s
0m00.18s | Tactics                                                   | 0m00.20s || -0m00.02s
0m00.18s | Tests                                                     | 0m00.12s || +0m00.06s
0m00.18s | hit/Truncations                                           | 0m00.23s || -0m00.05s
0m00.17s | categories/IndiscreteCategory                             | 0m00.16s || +0m00.01s
0m00.17s | Basics/Trunc                                              | 0m00.16s || +0m00.01s
0m00.17s | categories/HomFunctor                                     | 0m00.17s || +0m00.00s
0m00.17s | HProp                                                     | 0m00.20s || -0m00.03s
0m00.17s | categories/Pseudofunctor/Core                             | 0m00.17s || +0m00.00s
0m00.17s | categories/Structure/Core                                 | 0m00.22s || -0m00.04s
0m00.17s | categories/FunctorCategory/Dual                           | 0m00.16s || +0m00.01s
0m00.17s | categories/KanExtensions/Functors                         | 0m00.21s || -0m00.03s
0m00.16s | categories/Utf8                                           | 0m00.15s || +0m00.01s
0m00.16s | categories/FunctorCategory/Utf8                           | 0m00.11s || +0m00.05s
0m00.16s | categories/Functor/Prod/Functorial                        | 0m00.22s || -0m00.06s
0m00.16s | categories/Category/Sigma/OnObjects                       | 0m00.18s || -0m00.01s
0m00.16s | categories/NatCategory                                    | 0m00.15s || +0m00.01s
0m00.16s | Types/Forall                                              | 0m00.20s || -0m00.04s
0m00.16s | categories/Comma/Projection                               | 0m00.17s || -0m00.01s
0m00.15s | categories/Cat/Core                                       | 0m00.17s || -0m00.02s
0m00.15s | categories/Category/Prod                                  | 0m00.14s || +0m00.00s
0m00.15s | Types/Arrow                                               | 0m00.15s || +0m00.00s
0m00.15s | categories/Notations                                      | 0m00.14s || +0m00.00s
0m00.14s | Basics/Overture                                           | 0m00.12s || +0m00.02s
0m00.14s | UnivalenceImpliesFunext                                   | 0m00.14s || +0m00.00s
0m00.14s | categories/ExponentialLaws/Law3/Functors                  | 0m00.16s || -0m00.01s
0m00.14s | hit/Suspension                                            | 0m00.14s || +0m00.00s
0m00.14s | categories/Functor/Utf8                                   | 0m00.15s || -0m00.00s
0m00.14s | categories/NaturalTransformation/Utf8                     | 0m00.12s || +0m00.02s
0m00.14s | categories/Functor/Composition                            | 0m00.12s || +0m00.02s
0m00.13s | hit/iso                                                   | 0m00.13s || +0m00.00s
0m00.13s | categories/Adjoint/Hom                                    | 0m00.14s || -0m00.01s
0m00.13s | categories/FunctorCategory/Functorial                     | 0m00.18s || -0m00.04s
0m00.12s | categories/NaturalTransformation/Sum                      | 0m00.13s || -0m00.01s
0m00.12s | hit/unique_choice                                         | 0m00.08s || +0m00.03s
0m00.12s | Types/Bool                                                | 0m00.10s || +0m00.01s
0m00.12s | categories/KanExtensions/Core                             | 0m00.16s || -0m00.04s
0m00.12s | categories/Adjoint/UnitCounit                             | 0m00.12s || +0m00.00s
0m00.11s | categories/Comma                                          | 0m00.12s || -0m00.00s
0m00.11s | categories/Grothendieck/ToCat                             | 0m00.11s || +0m00.00s
0m00.11s | categories/Pseudofunctor                                  | 0m00.11s || +0m00.00s
0m00.11s | categories/InitialTerminalCategory/NaturalTransformations | 0m00.10s || +0m00.00s
0m00.11s | categories/Adjoint                                        | 0m00.12s || -0m00.00s
0m00.11s | Utf8                                                      | 0m00.09s || +0m00.02s
0m00.11s | categories/NaturalTransformation/Composition/Core         | 0m00.10s || +0m00.00s
0m00.10s | categories/Functor/Composition/Functorial                 | 0m00.11s || -0m00.00s
0m00.10s | categories/Category                                       | 0m00.10s || +0m00.00s
0m00.10s | categories/LaxComma                                       | 0m00.10s || +0m00.00s
0m00.10s | Functorish                                                | 0m00.08s || +0m00.02s
0m00.10s | categories/Functor/Notations                              | 0m00.15s || -0m00.04s
0m00.10s | categories/GroupoidCategory/Core                          | 0m00.09s || +0m00.01s
0m00.10s | categories/Category/Objects                               | 0m00.11s || -0m00.00s
0m00.10s | categories/LaxComma/Utf8                                  | 0m00.08s || +0m00.02s
0m00.10s | Basics/FunextVarieties                                    | 0m00.08s || +0m00.02s
0m00.10s | categories/NaturalTransformation/Identity                 | 0m00.10s || +0m00.00s
0m00.10s | categories/NaturalTransformation/Composition/Functorial   | 0m00.10s || +0m00.00s
0m00.10s | categories/Adjoint/Composition                            | 0m00.09s || +0m00.01s
0m00.09s | Conjugation                                               | 0m00.08s || +0m00.00s
0m00.09s | categories/DependentProduct                               | 0m00.09s || +0m00.00s
0m00.09s | categories/LaxComma/Notations                             | 0m00.09s || +0m00.00s
0m00.09s | categories/ExponentialLaws                                | 0m00.08s || +0m00.00s
0m00.09s | categories/Grothendieck                                   | 0m00.08s || +0m00.00s
0m00.09s | categories/Category/Univalent                             | 0m00.06s || +0m00.03s
0m00.09s | categories/FunctorCategory                                | 0m00.08s || +0m00.00s
0m00.09s | categories/Cat/Morphisms                                  | 0m00.10s || -0m00.01s
0m00.09s | categories/SetCategory/Functors/SetProp                   | 0m00.10s || -0m00.01s
0m00.08s | categories/Comma/Utf8                                     | 0m00.09s || -0m00.00s
0m00.08s | categories/DiscreteCategory                               | 0m00.06s || +0m00.02s
0m00.08s | categories/Profunctor/Core                                | 0m00.05s || +0m00.03s
0m00.08s | hit/Interval                                              | 0m00.08s || +0m00.00s
0m00.08s | categories/PseudonaturalTransformation                    | 0m00.09s || -0m00.00s
0m00.08s | categories/ExponentialLaws/Law1                           | 0m00.06s || +0m00.02s
0m00.08s | categories/ExponentialLaws/Law2                           | 0m00.05s || +0m00.03s
0m00.08s | coq/Init/Peano                                            | 0m00.09s || -0m00.00s
0m00.08s | categories/InitialTerminalCategory/Core                   | 0m00.08s || +0m00.00s
0m00.08s | categories/Adjoint/Identity                               | 0m00.06s || +0m00.02s
0m00.08s | categories/CategoryOfGroupoids                            | 0m00.08s || +0m00.00s
0m00.08s | categories/Functor/Pointwise                              | 0m00.06s || +0m00.02s
0m00.08s | categories/Adjoint/Notations                              | 0m00.06s || +0m00.02s
0m00.08s | categories/InitialTerminalCategory/Notations              | 0m00.06s || +0m00.02s
0m00.08s | categories/NaturalTransformation                          | 0m00.11s || -0m00.03s
0m00.08s | categories/KanExtensions                                  | 0m00.08s || +0m00.00s
0m00.08s | categories/SetCategory                                    | 0m00.06s || +0m00.02s
0m00.08s | Types/Record                                              | 0m00.08s || +0m00.00s
0m00.08s | categories/Limits                                         | 0m00.10s || -0m00.02s
0m00.08s | categories/Category/Pi                                    | 0m00.10s || -0m00.02s
0m00.08s | categories/FunctorCategory/Core                           | 0m00.09s || -0m00.00s
0m00.07s | categories/Adjoint/Utf8                                   | 0m00.08s || -0m00.00s
0m00.07s | categories/Adjoint/Dual                                   | 0m00.08s || -0m00.00s
0m00.07s | categories/Profunctor                                     | 0m00.08s || -0m00.00s
0m00.07s | categories/Functor/Dual                                   | 0m00.06s || +0m00.01s
0m00.07s | categories/ExponentialLaws/Tactics                        | 0m00.06s || +0m00.01s
0m00.07s | categories/ExponentialLaws/Law3                           | 0m00.08s || -0m00.00s
0m00.07s | categories/Functor/Prod                                   | 0m00.08s || -0m00.00s
0m00.07s | categories/NaturalTransformation/Composition              | 0m00.05s || +0m00.02s
0m00.07s | categories/Profunctor/Representable                       | 0m00.07s || +0m00.00s
0m00.07s | categories/Structure                                      | 0m00.06s || +0m00.01s
0m00.07s | Tactics/BinderApply                                       | 0m00.05s || +0m00.02s
0m00.07s | categories/Profunctor/Identity                            | 0m00.06s || +0m00.01s
0m00.07s | categories/SetCategory/Core                               | 0m00.08s || -0m00.00s
0m00.07s | categories/Adjoint/Composition/LawsTactic                 | 0m00.08s || -0m00.00s
0m00.07s | categories/NaturalTransformation/Core                     | 0m00.08s || -0m00.00s
0m00.06s | categories/Adjoint/Core                                   | 0m00.08s || -0m00.02s
0m00.06s | categories/Category/Utf8                                  | 0m00.06s || +0m00.00s
0m00.06s | categories/Category/Sigma                                 | 0m00.06s || +0m00.00s
0m00.06s | categories/NaturalTransformation/Notations                | 0m00.06s || +0m00.00s
0m00.06s | categories/Cat                                            | 0m00.07s || -0m00.01s
0m00.06s | categories/InitialTerminalCategory                        | 0m00.09s || -0m00.03s
0m00.06s | categories/Category/Dual                                  | 0m00.06s || +0m00.00s
0m00.06s | categories/Profunctor/Notations                           | 0m00.06s || +0m00.00s
0m00.06s | categories/ExponentialLaws/Law4                           | 0m00.07s || -0m00.01s
0m00.06s | categories/Category/Subcategory                           | 0m00.07s || -0m00.01s
0m00.06s | Types/Unit                                                | 0m00.07s || -0m00.01s
0m00.06s | categories/NaturalTransformation/Dual                     | 0m00.06s || +0m00.00s
0m00.06s | categories/Comma/Notations                                | 0m00.05s || +0m00.00s
0m00.06s | categories/Category/Subcategory/Wide                      | 0m00.07s || -0m00.01s
0m00.06s | categories/Category/Core                                  | 0m00.06s || +0m00.00s
0m00.06s | hit/TwoSphere                                             | 0m00.06s || +0m00.00s
0m00.06s | UnivalenceAxiom                                           | 0m00.05s || +0m00.00s
0m00.06s | categories/GroupoidCategory                               | 0m00.08s || -0m00.02s
0m00.05s | categories/SetCategory/Functors                           | 0m00.06s || -0m00.00s
0m00.05s | categories/Category/Strict                                | 0m00.04s || +0m00.01s
0m00.05s | Basics/Contractible                                       | 0m00.06s || -0m00.00s
0m00.05s | Misc                                                      | 0m00.05s || +0m00.00s
0m00.05s | hit/IntervalImpliesFunext                                 | 0m00.05s || +0m00.00s
0m00.05s | categories/CategoryOfSections                             | 0m00.05s || +0m00.00s
0m00.05s | categories/Structure/Notations                            | 0m00.05s || +0m00.00s
0m00.05s | categories/Functor/Composition/Core                       | 0m00.04s || +0m00.01s
0m00.05s | Basics/Pointed                                            | 0m00.04s || +0m00.01s
0m00.05s | categories/Category/Notations                             | 0m00.08s || -0m00.03s
0m00.05s | categories/Category/Subcategory/Full                      | 0m00.05s || +0m00.00s
0m00.05s | categories/FunctorCategory/Notations                      | 0m00.07s || -0m00.02s
0m00.05s | categories/Profunctor/Utf8                                | 0m00.06s || -0m00.00s
0m00.04s | categories/Functor/Identity                               | 0m00.03s || +0m00.01s
0m00.04s | coq/Init/Datatypes                                        | 0m00.03s || +0m00.01s
0m00.04s | categories/Functor/Core                                   | 0m00.04s || +0m00.00s
0m00.04s | Types                                                     | 0m00.06s || -0m00.01s
0m00.04s | coq/Init/Logic_Type                                       | 0m00.04s || +0m00.00s
0m00.04s | NullHomotopy                                              | 0m00.06s || -0m00.01s
0m00.04s | Types/Nat                                                 | 0m00.05s || -0m00.01s
0m00.04s | coq/Program/Tactics                                       | 0m00.04s || +0m00.00s
0m00.04s | categories/Structure/Utf8                                 | 0m00.05s || -0m00.01s
0m00.04s | Basics                                                    | 0m00.04s || +0m00.00s
0m00.03s | coq/Init/Notations                                        | 0m00.03s || +0m00.00s
0m00.03s | Basics/UniverseLevel                                      | 0m00.04s || -0m00.01s
0m00.03s | coq/Unicode/Utf8                                          | 0m00.03s || +0m00.00s
0m00.03s | Types/Empty                                               | 0m00.05s || -0m00.02s
0m00.03s | FunextAxiom                                               | 0m00.03s || +0m00.00s
0m00.02s | coq/Init/Specif                                           | 0m00.04s || -0m00.02s
0m00.02s | coq/Init/Logic                                            | 0m00.01s || +0m00.01s
0m00.02s | coq/Unicode/Utf8_core                                     | 0m00.03s || -0m00.00s
0m00.02s | coq/Init/Prelude                                          | 0m00.02s || +0m00.00s
0m00.01s | coq/Bool/Bool                                             | 0m00.01s || +0m00.00s
0m00.00s | coq/Init/Tactics                                          | 0m00.02s || -0m00.02s
missing word in comment
document use of `Check` for universe parameters
Reindent hit/quotient

I want to use it as an example, so I'd like to have it nicely indented
so that it's clear where the private inductive module ends.
Link to Dan Licata's blog post in STYLE.md
Merge pull request #618 from JasonGross/link-dan-licata

Link to Dan Licata's blog post in STYLE.md
Merge pull request #617 from JasonGross/reindent-quotient

Reindent hit/quotient
more checked universe documentation, in Extensions
use simple_induction in one more place
nullification versions of open and closed modalities
define `merely` using `Trunc` rather than `Tr`
Merge pull request #614 from mikeshulman/modules

Use modules for reflective subuniverses and modalities