├── .github ├── dependabot.yml └── workflows │ └── ci-ubuntu.yml ├── .gitignore ├── .mailmap ├── CHANGELOG-0.3.0.md ├── CITATION.cff ├── LICENSE ├── Makefile ├── README.md ├── README └── KanComplexes.md ├── agda-categories.agda-lib ├── src ├── Categories │ ├── 2-Category.agda │ ├── 2-Functor.agda │ ├── Adjoint.agda │ ├── Adjoint │ │ ├── AFT.agda │ │ ├── AFT │ │ │ └── SolutionSet.agda │ │ ├── Alternatives.agda │ │ ├── Compose.agda │ │ ├── Construction │ │ │ ├── CoEilenbergMoore.agda │ │ │ ├── CoKleisli.agda │ │ │ ├── EilenbergMoore.agda │ │ │ └── Kleisli.agda │ │ ├── Equivalence.agda │ │ ├── Equivalents.agda │ │ ├── Instance │ │ │ ├── 0-Truncation.agda │ │ │ ├── 01-Truncation.agda │ │ │ ├── BaseChange.agda │ │ │ ├── Core.agda │ │ │ ├── PathsOf.agda │ │ │ ├── PosetCore.agda │ │ │ ├── Slice.agda │ │ │ ├── StrictCore.agda │ │ │ └── StrictDiscrete.agda │ │ ├── Mate.agda │ │ ├── Monadic.agda │ │ ├── Monadic │ │ │ ├── Crude.agda │ │ │ └── Properties.agda │ │ ├── Parametric.agda │ │ ├── Properties.agda │ │ ├── RAPL.agda │ │ ├── Relative.agda │ │ ├── TwoSided.agda │ │ └── TwoSided │ │ │ └── Compose.agda │ ├── Bicategory.agda │ ├── Bicategory │ │ ├── Bigroupoid.agda │ │ ├── Construction │ │ │ ├── 1-Category.agda │ │ │ ├── LaxSlice.agda │ │ │ ├── Spans.agda │ │ │ └── Spans │ │ │ │ └── Properties.agda │ │ ├── Extras.agda │ │ ├── Instance │ │ │ ├── Cats.agda │ │ │ └── EnrichedCats.agda │ │ ├── LocalCoequalizers.agda │ │ ├── Monad.agda │ │ ├── Monad │ │ │ ├── Bimodule.agda │ │ │ ├── Bimodule │ │ │ │ └── Homomorphism.agda │ │ │ └── Properties.agda │ │ ├── Object │ │ │ ├── Product.agda │ │ │ └── Terminal.agda │ │ └── Opposite.agda │ ├── Category.agda │ ├── Category │ │ ├── BicartesianClosed.agda │ │ ├── BinaryProducts.agda │ │ ├── CMonoidEnriched.agda │ │ ├── Cartesian.agda │ │ ├── Cartesian │ │ │ ├── Bundle.agda │ │ │ ├── Monoidal.agda │ │ │ ├── Properties.agda │ │ │ └── SymmetricMonoidal.agda │ │ ├── CartesianClosed.agda │ │ ├── CartesianClosed │ │ │ ├── Bundle.agda │ │ │ ├── Canonical.agda │ │ │ ├── Locally.agda │ │ │ ├── Locally │ │ │ │ └── Properties.agda │ │ │ └── Properties.agda │ │ ├── Closed.agda │ │ ├── Cocartesian.agda │ │ ├── Cocartesian │ │ │ └── Bundle.agda │ │ ├── Cocomplete.agda │ │ ├── Cocomplete │ │ │ ├── Finitely.agda │ │ │ ├── Finitely │ │ │ │ └── Properties.agda │ │ │ ├── Properties.agda │ │ │ └── Properties │ │ │ │ └── Construction.agda │ │ ├── Complete.agda │ │ ├── Complete │ │ │ ├── Finitely.agda │ │ │ ├── Finitely │ │ │ │ └── Properties.agda │ │ │ ├── Properties.agda │ │ │ └── Properties │ │ │ │ ├── Construction.agda │ │ │ │ └── SolutionSet.agda │ │ ├── Concrete.agda │ │ ├── Concrete │ │ │ └── Properties.agda │ │ ├── Construction │ │ │ ├── 0-Groupoid.agda │ │ │ ├── Adjoints.agda │ │ │ ├── Arrow.agda │ │ │ ├── Bimodules.agda │ │ │ ├── Bimodules │ │ │ │ └── Properties.agda │ │ │ ├── CoEilenbergMoore.agda │ │ │ ├── CoKleisli.agda │ │ │ ├── Cocones.agda │ │ │ ├── Comma.agda │ │ │ ├── Cones.agda │ │ │ ├── Coproduct.agda │ │ │ ├── Core.agda │ │ │ ├── Cowedges.agda │ │ │ ├── DaggerFunctors.agda │ │ │ ├── EilenbergMoore.agda │ │ │ ├── Elements.agda │ │ │ ├── EnrichedFunctors.agda │ │ │ ├── F-Algebras.agda │ │ │ ├── F-Coalgebras.agda │ │ │ ├── Fin.agda │ │ │ ├── Functors.agda │ │ │ ├── Grothendieck.agda │ │ │ ├── GroupAsCategory.agda │ │ │ ├── Groups.agda │ │ │ ├── KanComplex.agda │ │ │ ├── KaroubiEnvelope.agda │ │ │ ├── KaroubiEnvelope │ │ │ │ └── Properties.agda │ │ │ ├── Kleisli.agda │ │ │ ├── LT-Models.agda │ │ │ ├── MonoidAsCategory.agda │ │ │ ├── MonoidalFunctors.agda │ │ │ ├── Monoids.agda │ │ │ ├── ObjectRestriction.agda │ │ │ ├── Path.agda │ │ │ ├── PathCategory.agda │ │ │ ├── Presheaves.agda │ │ │ ├── Properties │ │ │ │ ├── CoEilenbergMoore.agda │ │ │ │ ├── CoKleisli.agda │ │ │ │ ├── Comma.agda │ │ │ │ ├── EilenbergMoore.agda │ │ │ │ ├── Functors.agda │ │ │ │ ├── Kleisli.agda │ │ │ │ ├── Presheaves.agda │ │ │ │ └── Presheaves │ │ │ │ │ ├── Cartesian.agda │ │ │ │ │ ├── CartesianClosed.agda │ │ │ │ │ ├── Complete.agda │ │ │ │ │ └── FromCartesianCCC.agda │ │ │ ├── Pullbacks.agda │ │ │ ├── SetoidDiscrete.agda │ │ │ ├── Spans.agda │ │ │ ├── StrictDiscrete.agda │ │ │ ├── SymmetricMonoidalFunctors.agda │ │ │ ├── Thin.agda │ │ │ ├── TwistedArrow.agda │ │ │ ├── Wedges.agda │ │ │ └── mu-Bialgebras.agda │ │ ├── Core.agda │ │ ├── Dagger.agda │ │ ├── Dagger │ │ │ ├── Construction │ │ │ │ ├── DaggerFunctors.agda │ │ │ │ └── Discrete.agda │ │ │ └── Instance │ │ │ │ └── Rels.agda │ │ ├── Diagram │ │ │ └── Span.agda │ │ ├── Discrete.agda │ │ ├── Distributive.agda │ │ ├── Distributive │ │ │ └── Properties.agda │ │ ├── Duality.agda │ │ ├── Equivalence.agda │ │ ├── Equivalence │ │ │ ├── Preserves.agda │ │ │ └── Properties.agda │ │ ├── Exact.agda │ │ ├── Extensive.agda │ │ ├── Extensive │ │ │ ├── Bundle.agda │ │ │ └── Properties │ │ │ │ └── Distributive.agda │ │ ├── Finite.agda │ │ ├── Finite │ │ │ ├── Fin.agda │ │ │ └── Fin │ │ │ │ ├── Construction │ │ │ │ ├── Discrete.agda │ │ │ │ └── Poset.agda │ │ │ │ └── Instance │ │ │ │ ├── Parallel.agda │ │ │ │ ├── Span.agda │ │ │ │ └── Triangle.agda │ │ ├── Groupoid.agda │ │ ├── Groupoid │ │ │ └── Properties.agda │ │ ├── Helper.agda │ │ ├── Indiscrete.agda │ │ ├── Instance │ │ │ ├── Cartesians.agda │ │ │ ├── Cats.agda │ │ │ ├── DagCats.agda │ │ │ ├── EmptySet.agda │ │ │ ├── FamilyOfSetoids.agda │ │ │ ├── FinCatShapes.agda │ │ │ ├── FinSetoids.agda │ │ │ ├── Globe.agda │ │ │ ├── Groupoids.agda │ │ │ ├── KanComplexes.agda │ │ │ ├── LawvereTheories.agda │ │ │ ├── Monoidals.agda │ │ │ ├── Nat.agda │ │ │ ├── One.agda │ │ │ ├── PartialFunctions.agda │ │ │ ├── PointedSets.agda │ │ │ ├── Posets.agda │ │ │ ├── Preds.agda │ │ │ ├── Properties │ │ │ │ ├── Cats.agda │ │ │ │ ├── Posets.agda │ │ │ │ ├── Setoids.agda │ │ │ │ └── Setoids │ │ │ │ │ ├── CCC.agda │ │ │ │ │ ├── Choice.agda │ │ │ │ │ ├── Cocomplete.agda │ │ │ │ │ ├── Complete.agda │ │ │ │ │ ├── Exact.agda │ │ │ │ │ ├── Extensive.agda │ │ │ │ │ ├── LCCC.agda │ │ │ │ │ └── Limits │ │ │ │ │ └── Canonical.agda │ │ │ ├── Quivers.agda │ │ │ ├── Rels.agda │ │ │ ├── Setoids.agda │ │ │ ├── Sets.agda │ │ │ ├── Simplex.agda │ │ │ ├── SimplicialSet.agda │ │ │ ├── SimplicialSet │ │ │ │ └── Properties.agda │ │ │ ├── SingletonSet.agda │ │ │ ├── Span.agda │ │ │ ├── StrictCats.agda │ │ │ ├── StrictGroupoids.agda │ │ │ ├── Zero.agda │ │ │ └── Zero │ │ │ │ ├── Core.agda │ │ │ │ └── Properties.agda │ │ ├── Inverse.agda │ │ ├── Lift.agda │ │ ├── Lift │ │ │ └── Properties.agda │ │ ├── Monoidal.agda │ │ ├── Monoidal │ │ │ ├── Braided.agda │ │ │ ├── Braided │ │ │ │ └── Properties.agda │ │ │ ├── Bundle.agda │ │ │ ├── Closed.agda │ │ │ ├── Closed │ │ │ │ ├── IsClosed.agda │ │ │ │ └── IsClosed │ │ │ │ │ ├── Diagonal.agda │ │ │ │ │ ├── Dinatural.agda │ │ │ │ │ ├── Identity.agda │ │ │ │ │ ├── L.agda │ │ │ │ │ └── Pentagon.agda │ │ │ ├── CompactClosed.agda │ │ │ ├── Construction │ │ │ │ ├── Endofunctors.agda │ │ │ │ ├── Kleisli.agda │ │ │ │ ├── Kleisli │ │ │ │ │ ├── CounitalCopy.agda │ │ │ │ │ └── Symmetric.agda │ │ │ │ ├── Minus2.agda │ │ │ │ ├── Product.agda │ │ │ │ └── Reverse.agda │ │ │ ├── Core.agda │ │ │ ├── CounitalCopy.agda │ │ │ ├── CounitalCopy │ │ │ │ └── Restriction.agda │ │ │ ├── Instance │ │ │ │ ├── Cats.agda │ │ │ │ ├── One.agda │ │ │ │ ├── Rels.agda │ │ │ │ ├── Setoids.agda │ │ │ │ ├── Sets.agda │ │ │ │ └── StrictCats.agda │ │ │ ├── Interchange.agda │ │ │ ├── Interchange │ │ │ │ ├── Braided.agda │ │ │ │ └── Symmetric.agda │ │ │ ├── Properties.agda │ │ │ ├── Reasoning.agda │ │ │ ├── Rigid.agda │ │ │ ├── Star-Autonomous.agda │ │ │ ├── Symmetric.agda │ │ │ ├── Symmetric │ │ │ │ └── Properties.agda │ │ │ ├── Traced.agda │ │ │ └── Utilities.agda │ │ ├── Product.agda │ │ ├── Product │ │ │ └── Properties.agda │ │ ├── Regular.agda │ │ ├── Restriction.agda │ │ ├── Restriction │ │ │ ├── Construction │ │ │ │ ├── Kleisli.agda │ │ │ │ └── Trivial.agda │ │ │ ├── Instance │ │ │ │ └── PartialFunctions.agda │ │ │ ├── Properties.agda │ │ │ └── Properties │ │ │ │ └── Poset.agda │ │ ├── RigCategory.agda │ │ ├── Site.agda │ │ ├── Slice.agda │ │ ├── Slice │ │ │ └── Properties.agda │ │ ├── Species.agda │ │ ├── Species │ │ │ └── Constructions.agda │ │ ├── SubCategory.agda │ │ ├── Topos.agda │ │ ├── Unbundled.agda │ │ └── Unbundled │ │ │ ├── Properties.agda │ │ │ └── Utilities.agda │ ├── CoYoneda.agda │ ├── Comonad.agda │ ├── Comonad │ │ ├── Construction │ │ │ └── CoKleisli.agda │ │ ├── Distributive.agda │ │ ├── Morphism.agda │ │ └── Relative.agda │ ├── Diagram │ │ ├── Cocone.agda │ │ ├── Cocone │ │ │ └── Properties.agda │ │ ├── Coend.agda │ │ ├── Coend │ │ │ ├── Colimit.agda │ │ │ └── Properties.agda │ │ ├── Coequalizer.agda │ │ ├── Coequalizer │ │ │ └── Properties.agda │ │ ├── Colimit.agda │ │ ├── Colimit │ │ │ ├── DualProperties.agda │ │ │ ├── Lan.agda │ │ │ └── Properties.agda │ │ ├── Cone.agda │ │ ├── Cone │ │ │ └── Properties.agda │ │ ├── Cowedge.agda │ │ ├── Cowedge │ │ │ └── Properties.agda │ │ ├── Duality.agda │ │ ├── Empty.agda │ │ ├── End.agda │ │ ├── End │ │ │ ├── Fubini.agda │ │ │ ├── Instance │ │ │ │ └── NaturalTransformations.agda │ │ │ ├── Instances │ │ │ │ └── NaturalTransformation.agda │ │ │ ├── Limit.agda │ │ │ ├── Parameterized.agda │ │ │ └── Properties.agda │ │ ├── Equalizer.agda │ │ ├── Equalizer │ │ │ ├── Indexed.agda │ │ │ ├── Limit.agda │ │ │ └── Properties.agda │ │ ├── Finite.agda │ │ ├── KernelPair.agda │ │ ├── Limit.agda │ │ ├── Limit │ │ │ ├── Properties.agda │ │ │ └── Ran.agda │ │ ├── Pullback.agda │ │ ├── Pullback │ │ │ ├── Limit.agda │ │ │ └── Properties.agda │ │ ├── Pushout.agda │ │ ├── Pushout │ │ │ ├── Colimit.agda │ │ │ └── Properties.agda │ │ ├── ReflexivePair.agda │ │ ├── SubobjectClassifier.agda │ │ ├── Wedge.agda │ │ └── Wedge │ │ │ └── Properties.agda │ ├── Double.agda │ ├── Double │ │ └── Core.agda │ ├── Enriched │ │ ├── Category.agda │ │ ├── Category │ │ │ ├── Opposite.agda │ │ │ └── Underlying.agda │ │ ├── Functor.agda │ │ ├── NaturalTransformation.agda │ │ ├── NaturalTransformation │ │ │ └── NaturalIsomorphism.agda │ │ └── Over │ │ │ ├── One.agda │ │ │ └── Setoids.agda │ ├── FreeObjects │ │ └── Free.agda │ ├── Functor.agda │ ├── Functor │ │ ├── Algebra.agda │ │ ├── Bialgebra.agda │ │ ├── Bifunctor.agda │ │ ├── Bifunctor │ │ │ └── Properties.agda │ │ ├── Cartesian.agda │ │ ├── Cartesian │ │ │ └── Properties.agda │ │ ├── CartesianClosed.agda │ │ ├── Coalgebra.agda │ │ ├── Construction │ │ │ ├── Constant.agda │ │ │ ├── Diagonal.agda │ │ │ ├── FromDiscrete.agda │ │ │ ├── LiftAlgebras.agda │ │ │ ├── LiftCoalgebras.agda │ │ │ ├── LiftSetoids.agda │ │ │ ├── Limit.agda │ │ │ ├── ObjectRestriction.agda │ │ │ ├── PathsOf.agda │ │ │ ├── SubCategory.agda │ │ │ ├── SubCategory │ │ │ │ └── Properties.agda │ │ │ └── Zero.agda │ │ ├── Core.agda │ │ ├── Dagger.agda │ │ ├── DistributiveLaw.agda │ │ ├── Duality.agda │ │ ├── Equivalence.agda │ │ ├── Fibration.agda │ │ ├── Groupoid.agda │ │ ├── Hom.agda │ │ ├── Hom │ │ │ ├── Properties.agda │ │ │ └── Properties │ │ │ │ ├── Contra.agda │ │ │ │ └── Covariant.agda │ │ ├── IdentityOnObjects.agda │ │ ├── Instance │ │ │ ├── 0-Truncation.agda │ │ │ ├── 01-Truncation.agda │ │ │ ├── ConnectedComponents.agda │ │ │ ├── Core.agda │ │ │ ├── Discrete.agda │ │ │ ├── SetoidDiscrete.agda │ │ │ ├── StrictCore.agda │ │ │ ├── Twisted.agda │ │ │ └── UnderlyingQuiver.agda │ │ ├── Limits.agda │ │ ├── Monoidal.agda │ │ ├── Monoidal │ │ │ ├── Braided.agda │ │ │ ├── Construction │ │ │ │ └── Product.agda │ │ │ ├── PointwiseTensor.agda │ │ │ ├── Properties.agda │ │ │ ├── Symmetric.agda │ │ │ └── Tensor.agda │ │ ├── Power.agda │ │ ├── Power │ │ │ ├── Functorial.agda │ │ │ └── NaturalTransformation.agda │ │ ├── Presheaf.agda │ │ ├── Profunctor.agda │ │ ├── Profunctor │ │ │ ├── Cograph.agda │ │ │ └── FormalComposite.agda │ │ ├── Properties.agda │ │ ├── Representable.agda │ │ ├── Restriction.agda │ │ ├── Slice.agda │ │ └── Slice │ │ │ └── BaseChange.agda │ ├── GlobularSet.agda │ ├── Kan.agda │ ├── Kan │ │ └── Duality.agda │ ├── Minus2-Category.agda │ ├── Minus2-Category │ │ ├── Construction │ │ │ └── Indiscrete.agda │ │ ├── Instance │ │ │ └── One.agda │ │ └── Properties.agda │ ├── Monad.agda │ ├── Monad │ │ ├── Commutative.agda │ │ ├── Commutative │ │ │ └── Properties.agda │ │ ├── Construction │ │ │ └── Kleisli.agda │ │ ├── Distributive.agda │ │ ├── Duality.agda │ │ ├── EquationalLifting.agda │ │ ├── Graded.agda │ │ ├── Idempotent.agda │ │ ├── Morphism.agda │ │ ├── Relative.agda │ │ ├── Strong.agda │ │ └── Strong │ │ │ └── Properties.agda │ ├── Morphism.agda │ ├── Morphism │ │ ├── Cartesian.agda │ │ ├── Duality.agda │ │ ├── Extremal.agda │ │ ├── Extremal │ │ │ └── Properties.agda │ │ ├── HeterogeneousEquality.agda │ │ ├── HeterogeneousIdentity.agda │ │ ├── HeterogeneousIdentity │ │ │ └── Properties.agda │ │ ├── Idempotent.agda │ │ ├── Idempotent │ │ │ └── Bundles.agda │ │ ├── IsoEquiv.agda │ │ ├── Isomorphism.agda │ │ ├── Lifts.agda │ │ ├── Lifts │ │ │ └── Properties.agda │ │ ├── Normal.agda │ │ ├── Notation.agda │ │ ├── Properties.agda │ │ ├── Reasoning.agda │ │ ├── Reasoning │ │ │ ├── Core.agda │ │ │ └── Iso.agda │ │ ├── Regular.agda │ │ ├── Regular │ │ │ └── Properties.agda │ │ └── Universal.agda │ ├── Multi │ │ └── Category │ │ │ └── Indexed.agda │ ├── NaturalTransformation.agda │ ├── NaturalTransformation │ │ ├── Core.agda │ │ ├── Dinatural.agda │ │ ├── Equivalence.agda │ │ ├── Extranatural.agda │ │ ├── Hom.agda │ │ ├── Monoidal.agda │ │ ├── Monoidal │ │ │ ├── Braided.agda │ │ │ └── Symmetric.agda │ │ ├── NaturalIsomorphism.agda │ │ ├── NaturalIsomorphism │ │ │ ├── Equivalence.agda │ │ │ ├── Functors.agda │ │ │ ├── Monoidal.agda │ │ │ ├── Monoidal │ │ │ │ ├── Braided.agda │ │ │ │ └── Symmetric.agda │ │ │ └── Properties.agda │ │ └── Properties.agda │ ├── Object │ │ ├── Biproduct.agda │ │ ├── Cokernel.agda │ │ ├── Coproduct.agda │ │ ├── Coproduct │ │ │ ├── Indexed.agda │ │ │ └── Indexed │ │ │ │ └── Properties.agda │ │ ├── Duality.agda │ │ ├── Exponential.agda │ │ ├── Group.agda │ │ ├── Initial.agda │ │ ├── Initial │ │ │ └── Colimit.agda │ │ ├── InternalRelation.agda │ │ ├── Kernel.agda │ │ ├── Kernel │ │ │ └── Properties.agda │ │ ├── Monoid.agda │ │ ├── NaturalNumbers.agda │ │ ├── NaturalNumbers │ │ │ ├── Parametrized.agda │ │ │ ├── Parametrized │ │ │ │ └── Properties │ │ │ │ │ └── F-Algebras.agda │ │ │ └── Properties │ │ │ │ ├── F-Algebras.agda │ │ │ │ └── Parametrized.agda │ │ ├── Product.agda │ │ ├── Product │ │ │ ├── Construction.agda │ │ │ ├── Core.agda │ │ │ ├── Indexed.agda │ │ │ ├── Indexed │ │ │ │ └── Properties.agda │ │ │ ├── Limit.agda │ │ │ └── Morphisms.agda │ │ ├── StrictInitial.agda │ │ ├── Subobject.agda │ │ ├── Subobject │ │ │ └── Properties.agda │ │ ├── Terminal.agda │ │ ├── Terminal │ │ │ └── Limit.agda │ │ └── Zero.agda │ ├── Pseudofunctor.agda │ ├── Pseudofunctor │ │ ├── Composition.agda │ │ ├── Hom.agda │ │ ├── Identity.agda │ │ └── Instance │ │ │ └── EnrichedUnderlying.agda │ ├── Tactic │ │ └── Category.agda │ ├── Theory │ │ ├── Lawvere.agda │ │ └── Lawvere 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