_CoqProject

-R theories HoTT
-Q contrib HoTT.Contrib

#-arg -boot
-arg -noinit
-arg -indices-matter

#
#   Table of contents:
#
#   # Basics
#   # Types
#   # Cubical
#   # Spaces
#   # Modalities
#   # HIT
#   # Colimits
#   # Diagrams
#   # Truncations
#   # Other
#   # Contrib
#   # Homotopy
#   # Pointed
#   # Spectra
#   # Algebra
#   # Tactics
#   # PropResizing
#   # Categories
#   # Classes
#

#
#   Basics
#

theories/Basics.v

theories/Basics/Notations.v
theories/Basics/Utf8.v

theories/Basics/Overture.v
theories/Basics/PathGroupoids.v
theories/Basics/UniverseLevel.v
theories/Basics/Contractible.v
theories/Basics/Equivalences.v
theories/Basics/Decidable.v
theories/Basics/Datatypes.v
theories/Basics/Logic.v

theories/Basics/Tactics.v

theories/Basics/Nat.v
theories/Basics/Trunc.v
theories/Basics/Numeral.v
theories/Basics/Decimal.v
theories/Basics/Hexadecimal.v


#
#   Wildcat
#

theories/WildCat.v
theories/WildCat/Core.v
theories/WildCat/UnitCat.v
theories/WildCat/EmptyCat.v
theories/WildCat/Prod.v
theories/WildCat/Equiv.v
theories/WildCat/Sum.v
theories/WildCat/Forall.v
theories/WildCat/Sigma.v
theories/WildCat/Opposite.v
theories/WildCat/Paths.v
theories/WildCat/Type.v
theories/WildCat/Induced.v
theories/WildCat/EquivGpd.v
theories/WildCat/FunctorCat.v
theories/WildCat/Yoneda.v
theories/WildCat/TwoOneCat.v
theories/WildCat/NatTrans.v
theories/WildCat/PointedCat.v
theories/WildCat/Square.v

#
#   Types
#

theories/Types.v

theories/Types/Paths.v
theories/Types/Unit.v
theories/Types/Forall.v
theories/Types/Arrow.v
theories/Types/Sigma.v
theories/Types/Prod.v
theories/Types/Empty.v
theories/Types/Bool.v
theories/Types/Sum.v
theories/Types/Wtype.v
theories/Types/Equiv.v
theories/Types/Universe.v

#
#   Cubical
#

theories/Cubical.v

theories/Cubical/DPath.v
theories/Cubical/PathSquare.v
theories/Cubical/DPathSquare.v
theories/Cubical/PathCube.v
theories/Cubical/DPathCube.v

#
#   Spaces
#

theories/Spaces/Nat.v
theories/Spaces/List.v
theories/Spaces/Cantor.v

theories/Spaces/Finite/Fin.v
theories/Spaces/Finite/FinNat.v
theories/Spaces/Finite/FinInduction.v
theories/Spaces/Finite/Finite.v
theories/Spaces/Finite/FinSeq.v
theories/Spaces/Finite/Tactics.v
theories/Spaces/Finite.v

theories/Spaces/Universe.v
theories/Spaces/Card.v
theories/Spaces/Circle.v
theories/Spaces/TwoSphere.v
theories/Spaces/Spheres.v

theories/Spaces/Int.v
theories/Spaces/Int/Core.v
theories/Spaces/Int/Spec.v
theories/Spaces/Int/Equiv.v
theories/Spaces/Int/LoopExp.v

theories/Spaces/Pos.v
theories/Spaces/Pos/Core.v
theories/Spaces/Pos/Spec.v

theories/Spaces/BAut.v
theories/Spaces/BAut/Cantor.v
theories/Spaces/BAut/Bool.v
theories/Spaces/BAut/Bool/IncoherentIdempotent.v
theories/Spaces/BAut/Rigid.v

theories/Spaces/No.v
theories/Spaces/No/Core.v
theories/Spaces/No/Negation.v
theories/Spaces/No/Addition.v

theories/Spaces/Torus/Torus.v
theories/Spaces/Torus/TorusEquivCircles.v
theories/Spaces/Torus/TorusHomotopy.v

#
#   Modalities
#

theories/Modalities/ReflectiveSubuniverse.v
theories/Modalities/Modality.v
theories/Modalities/Accessible.v
theories/Modalities/Descent.v
theories/Modalities/Separated.v
theories/Modalities/Lex.v
theories/Modalities/Topological.v
theories/Modalities/Notnot.v
theories/Modalities/Identity.v
theories/Modalities/Localization.v
theories/Modalities/Nullification.v
theories/Modalities/Open.v
theories/Modalities/Closed.v
theories/Modalities/Fracture.v

theories/Modalities/CoreflectiveSubuniverse.v

#
#   HIT
#

theories/HIT/Coeq.v
theories/HIT/FreeIntQuotient.v
theories/HIT/Flattening.v
theories/HIT/Interval.v
theories/HIT/epi.v
theories/HIT/unique_choice.v
theories/HIT/surjective_factor.v
theories/HIT/quotient.v
theories/HIT/iso.v
theories/HIT/SetCone.v
theories/HIT/V.v

#
#   Limits
#

theories/Limits/Limit.v
theories/Limits/Equalizer.v
theories/Limits/Pullback.v

#
#   Colimits
#

theories/Colimits/Pushout.v
theories/Colimits/SpanPushout.v
theories/Colimits/MappingCylinder.v
theories/Colimits/Quotient.v

theories/Colimits/Colimit.v
theories/Colimits/Colimit_Sigma.v
theories/Colimits/Colimit_Prod.v
theories/Colimits/Colimit_Pushout.v
theories/Colimits/Colimit_Coequalizer.v
theories/Colimits/Colimit_Flattening.v
theories/Colimits/Colimit_Pushout_Flattening.v
theories/Colimits/Sequential.v

#
#   Diagrams
#

theories/Diagrams/Graph.v
theories/Diagrams/Diagram.v
theories/Diagrams/Cone.v
theories/Diagrams/Cocone.v
theories/Diagrams/DDiagram.v

theories/Diagrams/ConstantDiagram.v
theories/Diagrams/CommutativeSquares.v
theories/Diagrams/Sequence.v
theories/Diagrams/Span.v
theories/Diagrams/ParallelPair.v

#
#   Truncations
#

theories/Truncations.v

theories/Truncations/Core.v
theories/Truncations/Connectedness.v

#
#   Varieties of Equivalence
#

theories/Equiv/BiInv.v
theories/Equiv/PathSplit.v
theories/Equiv/Relational.v

#
#   Other
#

theories/BoundedSearch.v
theories/HFiber.v
theories/HProp.v
theories/Extensions.v
theories/HSet.v
theories/Projective.v
theories/TruncType.v
theories/DProp.v
theories/EquivGroupoids.v
theories/Functorish.v
theories/FunextAxiom.v
theories/UnivalenceAxiom.v
theories/ObjectClassifier.v
theories/NullHomotopy.v
theories/Idempotents.v
theories/Factorization.v
theories/Constant.v
theories/ExcludedMiddle.v
theories/Misc.v
theories/PathAny.v
theories/Utf8.v
theories/HoTT.v
theories/Tests.v

#
#   Metatheory
#
theories/Metatheory/Core.v
theories/Metatheory/FunextVarieties.v
theories/Metatheory/TruncImpliesFunext.v
theories/Metatheory/IntervalImpliesFunext.v
theories/Metatheory/UnivalenceImpliesFunext.v
theories/Metatheory/UnivalenceVarieties.v


#
#   Contrib
#

contrib/HoTTBook.v
contrib/HoTTBookExercises.v

#
#   Homotopy
#

theories/Homotopy/HomotopyGroup.v
theories/Homotopy/Pi1S1.v

theories/Homotopy/Suspension.v
theories/Homotopy/Smash.v
theories/Homotopy/Wedge.v
theories/Homotopy/Join.v

theories/Homotopy/WhiteheadsPrinciple.v
theories/Homotopy/HSpace.v
theories/Homotopy/HSpaceS1.v
theories/Homotopy/BlakersMassey.v
theories/Homotopy/Freudenthal.v
theories/Homotopy/ClassifyingSpace.v
theories/Homotopy/EMSpace.v
theories/Homotopy/CayleyDickson.v

theories/Homotopy/SuccessorStructure.v
theories/Homotopy/ExactSequence.v

#
#   Pointed
#

theories/Pointed.v

theories/Pointed/Core.v
theories/Pointed/Loops.v
theories/Pointed/pMap.v
theories/Pointed/pFiber.v
theories/Pointed/pEquiv.v
theories/Pointed/pTrunc.v
theories/Pointed/pHomotopy.v
theories/Pointed/pSusp.v

#
#   Spectra
#

theories/Spectra/Spectrum.v
theories/Spectra/Coinductive.v

#
#   Universal Algebra
#

theories/Algebra/Universal/Algebra.v
theories/Algebra/Universal/Homomorphism.v
theories/Algebra/Universal/Operation.v
theories/Algebra/Universal/Congruence.v
theories/Algebra/Universal/TermAlgebra.v

#
#   Algebra
#

theories/Algebra/ooGroup.v
theories/Algebra/Aut.v
theories/Algebra/ooAction.v

theories/Algebra/Congruence.v

theories/Algebra/Rings.v
theories/Algebra/Rings/CRing.v
theories/Algebra/Rings/Ideal.v
theories/Algebra/Rings/QuotientRing.v
theories/Algebra/Rings/Z.v

theories/Algebra/AbGroups.v
theories/Algebra/AbGroups/AbelianGroup.v
theories/Algebra/AbGroups/Abelianization.v
theories/Algebra/AbGroups/AbPullback.v
theories/Algebra/AbGroups/AbPushout.v
theories/Algebra/AbGroups/Z.v

theories/Algebra/Groups.v
theories/Algebra/Groups/Group.v
theories/Algebra/Groups/Subgroup.v
theories/Algebra/Groups/QuotientGroup.v
theories/Algebra/Groups/Image.v
theories/Algebra/Groups/Kernel.v
theories/Algebra/Groups/GrpPullback.v
theories/Algebra/Groups/FreeProduct.v
theories/Algebra/Groups/GroupCoeq.v
theories/Algebra/Groups/Presentation.v
theories/Algebra/Groups/ShortExactSequence.v

theories/Algebra/Groups/FreeGroup.v

theories/Algebra/Groups/FreeGroup/ListQuotient.v
theories/Algebra/Groups/FreeGroup/LoopSusp.v

#
#   Tactics
#

theories/Tactics.v
theories/Tactics/BinderApply.v
theories/Tactics/EquivalenceInduction.v
theories/Tactics/EvalIn.v
theories/Tactics/Nameless.v
theories/Tactics/RewriteModuloAssociativity.v

#
#   PropResizing
#

theories/PropResizing/PropResizing.v
theories/PropResizing/ImpredicativeTruncation.v
theories/PropResizing/Nat.v

#
#   Categories
#

theories/Categories.v

theories/Categories/Category.v
theories/Categories/Functor.v
theories/Categories/NaturalTransformation.v

theories/Categories/Category/Core.v
theories/Categories/Functor/Core.v
theories/Categories/NaturalTransformation/Core.v

theories/Categories/Category/Morphisms.v
theories/Categories/Category/Strict.v
theories/Categories/Category/Univalent.v
theories/Categories/Category/Objects.v
theories/Categories/Category/Dual.v
theories/Categories/Category/Paths.v
theories/Categories/Category/Prod.v
theories/Categories/Category/Pi.v
theories/Categories/Category/Sum.v
theories/Categories/Category/Sigma.v
theories/Categories/Category/Sigma/Core.v

theories/Categories/Functor/Composition.v
theories/Categories/Functor/Composition/Core.v
theories/Categories/Functor/Identity.v
theories/Categories/Functor/Paths.v

theories/Categories/Category/Sigma/OnMorphisms.v
theories/Categories/Category/Sigma/OnObjects.v
theories/Categories/Category/Sigma/Univalent.v
theories/Categories/Category/Subcategory.v
theories/Categories/Category/Subcategory/Full.v
theories/Categories/Category/Subcategory/Wide.v
theories/Categories/Category/Notations.v
theories/Categories/Category/Utf8.v

theories/Categories/Functor/Prod.v
theories/Categories/Functor/Dual.v

theories/Categories/SetCategory.v
theories/Categories/SetCategory/Core.v
theories/Categories/SetCategory/Morphisms.v
theories/Categories/SetCategory/Functors.v
theories/Categories/SetCategory/Functors/SetProp.v

theories/Categories/SimplicialSets.v
theories/Categories/SemiSimplicialSets.v

theories/Categories/FundamentalPreGroupoidCategory.v
theories/Categories/HomotopyPreCategory.v

theories/Categories/HomFunctor.v
theories/Categories/Functor/Attributes.v

theories/Categories/NaturalTransformation/Paths.v
theories/Categories/NaturalTransformation/Identity.v
theories/Categories/NaturalTransformation/Composition.v
theories/Categories/NaturalTransformation/Composition/Core.v
theories/Categories/NaturalTransformation/Composition/Laws.v

theories/Categories/FunctorCategory.v
theories/Categories/FunctorCategory/Core.v

theories/Categories/NaturalTransformation/Composition/Functorial.v

theories/Categories/ExponentialLaws.v
theories/Categories/ExponentialLaws/Law0.v
theories/Categories/ExponentialLaws/Law1.v
theories/Categories/ExponentialLaws/Law1/Functors.v
theories/Categories/ExponentialLaws/Law1/Law.v
theories/Categories/ExponentialLaws/Law2.v
theories/Categories/ExponentialLaws/Law2/Functors.v
theories/Categories/ExponentialLaws/Law2/Law.v
theories/Categories/ExponentialLaws/Law3.v
theories/Categories/ExponentialLaws/Law3/Functors.v
theories/Categories/ExponentialLaws/Law3/Law.v
theories/Categories/ExponentialLaws/Law4.v
theories/Categories/ExponentialLaws/Law4/Functors.v
theories/Categories/ExponentialLaws/Law4/Law.v
theories/Categories/ExponentialLaws/Tactics.v

theories/Categories/Functor/Composition/Functorial.v
theories/Categories/Functor/Composition/Functorial/Core.v
theories/Categories/Functor/Composition/Functorial/Attributes.v
theories/Categories/Functor/Composition/Laws.v

theories/Categories/Functor/Sum.v
theories/Categories/Functor/Pointwise.v
theories/Categories/Functor/Prod/Core.v
theories/Categories/Functor/Prod/Universal.v

theories/Categories/GroupoidCategory.v
theories/Categories/GroupoidCategory/Core.v
theories/Categories/GroupoidCategory/Dual.v

theories/Categories/CategoryOfGroupoids.v

theories/Categories/DiscreteCategory.v

theories/Categories/IndiscreteCategory.v

theories/Categories/NatCategory.v
theories/Categories/ChainCategory.v

theories/Categories/InitialTerminalCategory.v
theories/Categories/InitialTerminalCategory/Core.v
theories/Categories/InitialTerminalCategory/Functors.v
theories/Categories/InitialTerminalCategory/NaturalTransformations.v
theories/Categories/InitialTerminalCategory/Pseudofunctors.v
theories/Categories/InitialTerminalCategory/Notations.v

theories/Categories/NaturalTransformation/Prod.v

theories/Categories/Functor/Prod/Functorial.v
theories/Categories/Functor/Pointwise/Core.v
theories/Categories/Functor/Pointwise/Properties.v
theories/Categories/Functor/Notations.v
theories/Categories/Functor/Utf8.v

theories/Categories/NaturalTransformation/Dual.v
theories/Categories/NaturalTransformation/Sum.v
theories/Categories/NaturalTransformation/Pointwise.v

theories/Categories/FunctorCategory/Dual.v
theories/Categories/FunctorCategory/Morphisms.v

theories/Categories/NaturalTransformation/Isomorphisms.v
theories/Categories/NaturalTransformation/Notations.v
theories/Categories/NaturalTransformation/Utf8.v

theories/Categories/Structure.v
theories/Categories/Structure/Core.v
theories/Categories/Structure/IdentityPrinciple.v
theories/Categories/Structure/Notations.v
theories/Categories/Structure/Utf8.v

theories/Categories/CategoryOfSections.v
theories/Categories/CategoryOfSections/Core.v

theories/Categories/Profunctor/Core.v
theories/Categories/Profunctor/Identity.v

theories/Categories/Comma.v
theories/Categories/Comma/Core.v

theories/Categories/Adjoint.v
theories/Categories/Adjoint/UnitCounit.v
theories/Categories/Adjoint/Core.v
theories/Categories/Adjoint/Paths.v
theories/Categories/Adjoint/Identity.v
theories/Categories/Adjoint/Composition.v
theories/Categories/Adjoint/Composition/Core.v
theories/Categories/Adjoint/Composition/LawsTactic.v
theories/Categories/Adjoint/Composition/AssociativityLaw.v
theories/Categories/Adjoint/Composition/IdentityLaws.v
theories/Categories/Adjoint/Dual.v
theories/Categories/Adjoint/UnitCounitCoercions.v
theories/Categories/Adjoint/UniversalMorphisms.v
theories/Categories/Adjoint/UniversalMorphisms/Core.v
theories/Categories/Adjoint/Functorial.v
theories/Categories/Adjoint/Functorial/Core.v
theories/Categories/Adjoint/Functorial/Parts.v
theories/Categories/Adjoint/Functorial/Laws.v
theories/Categories/Adjoint/Hom.v
theories/Categories/Adjoint/HomCoercions.v
theories/Categories/Adjoint/Pointwise.v
theories/Categories/Adjoint/Notations.v
theories/Categories/Adjoint/Utf8.v

theories/Categories/Cat.v
theories/Categories/Cat/Core.v

theories/Categories/DualFunctor.v

theories/Categories/FunctorCategory/Functorial.v
theories/Categories/FunctorCategory/Notations.v
theories/Categories/FunctorCategory/Utf8.v

theories/Categories/ProductLaws.v

theories/Categories/GroupoidCategory/Morphisms.v

theories/Categories/Profunctor.v
theories/Categories/Profunctor/Representable.v
theories/Categories/Profunctor/Notations.v
theories/Categories/Profunctor/Utf8.v

theories/Categories/Yoneda.v

theories/Categories/Cat/Morphisms.v

theories/Categories/Comma/Dual.v
theories/Categories/Comma/Projection.v
theories/Categories/Comma/InducedFunctors.v
theories/Categories/Comma/ProjectionFunctors.v
theories/Categories/Comma/Functorial.v
theories/Categories/Comma/Notations.v
theories/Categories/Comma/Utf8.v

theories/Categories/Pseudofunctor.v
theories/Categories/Pseudofunctor/Core.v
theories/Categories/Pseudofunctor/RewriteLaws.v
theories/Categories/Pseudofunctor/FromFunctor.v
theories/Categories/Pseudofunctor/Identity.v

theories/Categories/PseudonaturalTransformation.v
theories/Categories/PseudonaturalTransformation/Core.v

theories/Categories/LaxComma.v
theories/Categories/LaxComma/Core.v
theories/Categories/LaxComma/CoreParts.v
theories/Categories/LaxComma/CoreLaws.v
theories/Categories/LaxComma/Notations.v
theories/Categories/LaxComma/Utf8.v

theories/Categories/Grothendieck.v
theories/Categories/Grothendieck/ToSet.v
theories/Categories/Grothendieck/ToSet/Core.v
theories/Categories/Grothendieck/ToSet/Morphisms.v
theories/Categories/Grothendieck/ToSet/Univalent.v
theories/Categories/Grothendieck/PseudofunctorToCat.v
theories/Categories/Grothendieck/ToCat.v

theories/Categories/DependentProduct.v

theories/Categories/UniversalProperties.v

theories/Categories/KanExtensions.v
theories/Categories/KanExtensions/Core.v
theories/Categories/KanExtensions/Functors.v

theories/Categories/Limits.v
theories/Categories/Limits/Core.v
theories/Categories/Limits/Functors.v

theories/Categories/Notations.v
theories/Categories/Utf8.v

#
#   mathclasses
#

theories/Classes/tactics/ring_tac.v
theories/Classes/tactics/ring_quote.v
theories/Classes/tactics/ring_pol.v

theories/Classes/isomorphisms/rings.v

theories/Classes/orders/rings.v
theories/Classes/orders/maps.v
theories/Classes/orders/semirings.v
theories/Classes/orders/dec_fields.v
theories/Classes/orders/sum.v
theories/Classes/orders/lattices.v
theories/Classes/orders/naturals.v
theories/Classes/orders/orders.v
theories/Classes/orders/nat_int.v
theories/Classes/orders/integers.v
theories/Classes/orders/archimedean.v
theories/Classes/orders/fields.v

theories/Classes/implementations/assume_rationals.v
theories/Classes/implementations/peano_naturals.v
theories/Classes/implementations/binary_naturals.v
theories/Classes/implementations/natpair_integers.v
theories/Classes/implementations/field_of_fractions.v
theories/Classes/implementations/list.v
theories/Classes/implementations/bool.v
theories/Classes/implementations/hprop_lattice.v
theories/Classes/implementations/pointwise.v
theories/Classes/implementations/family_prod.v
theories/Classes/implementations/ne_list.v

theories/Classes/interfaces/monad.v
theories/Classes/interfaces/abstract_algebra.v
theories/Classes/interfaces/naturals.v
theories/Classes/interfaces/rationals.v
theories/Classes/interfaces/canonical_names.v
theories/Classes/interfaces/orders.v
theories/Classes/interfaces/archimedean.v
theories/Classes/interfaces/cauchy.v
theories/Classes/interfaces/round.v
theories/Classes/interfaces/integers.v
theories/Classes/interfaces/ua_algebra.v
theories/Classes/interfaces/ua_setalgebra.v
theories/Classes/interfaces/ua_congruence.v

theories/Classes/theory/premetric.v
theories/Classes/theory/int_abs.v
theories/Classes/theory/rings.v
theories/Classes/theory/additional_operations.v
theories/Classes/theory/apartness.v
theories/Classes/theory/dec_fields.v
theories/Classes/theory/lattices.v
theories/Classes/theory/naturals.v
theories/Classes/theory/nat_distance.v
theories/Classes/theory/groups.v
theories/Classes/theory/fields.v
theories/Classes/theory/rationals.v
theories/Classes/theory/integers.v
theories/Classes/theory/ua_homomorphism.v
theories/Classes/theory/ua_isomorphic.v
theories/Classes/theory/ua_prod_algebra.v
theories/Classes/theory/ua_subalgebra.v
theories/Classes/theory/ua_quotient_algebra.v
theories/Classes/theory/ua_first_isomorphism.v
theories/Classes/theory/ua_second_isomorphism.v
theories/Classes/theory/ua_third_isomorphism.v

theories/Classes/categories/ua_category.v

theories/Classes/tests/ring_tac.v

theories/Analysis/Locator.v