├── .editorconfig ├── .gitattributes ├── .github ├── pull_request_template.md └── workflows │ ├── build.yml │ └── preview.yml ├── .gitignore ├── 1lab.agda-lib ├── CITATION.bib ├── CODE_OF_CONDUCT.md ├── CONTRIBUTING.md ├── LICENSE ├── README.md ├── _typos.toml ├── cabal.project ├── default.nix ├── package.json ├── src ├── 1Lab │ ├── Classical.lagda.md │ ├── Counterexamples │ │ ├── GlobalChoice.lagda.md │ │ ├── IsIso.lagda.md │ │ ├── Isovalence.lagda.md │ │ ├── Russell.lagda.md │ │ └── Sigma.lagda.md │ ├── Equiv.lagda.md │ ├── Equiv │ │ ├── Biinv.lagda.md │ │ ├── Fibrewise.lagda.md │ │ ├── FromPath.lagda.md │ │ └── HalfAdjoint.lagda.md │ ├── Extensionality.agda │ ├── Function │ │ ├── Embedding.lagda.md │ │ ├── Reasoning.lagda.md │ │ └── Surjection.lagda.md │ ├── HLevel.lagda.md │ ├── HLevel │ │ ├── Closure.lagda.md │ │ └── Universe.lagda.md │ ├── Inductive.agda │ ├── Membership.agda │ ├── Path.lagda.md │ ├── Path │ │ ├── Cartesian.lagda.md │ │ ├── Groupoid.lagda.md │ │ ├── IdentitySystem.lagda.md │ │ ├── IdentitySystem │ │ │ ├── Interface.agda │ │ │ └── Strict.lagda.md │ │ └── Reasoning.lagda.md │ ├── Prelude.agda │ ├── Reflection.lagda.md │ ├── Reflection │ │ ├── Copattern.agda │ │ ├── Deriving │ │ │ └── Show.agda │ │ ├── HLevel.agda │ │ ├── Induction.agda │ │ ├── Induction │ │ │ └── Examples.agda │ │ ├── List.lagda.md │ │ ├── Marker.agda │ │ ├── Record.agda │ │ ├── Regularity.agda │ │ ├── Signature.agda │ │ ├── Solver.agda │ │ ├── Subst.agda │ │ ├── Univalence.agda │ │ └── Variables.agda │ ├── Resizing.lagda.md │ ├── Truncation.lagda.md │ ├── Type.lagda.md │ ├── Type │ │ ├── Pi.lagda.md │ │ ├── Pi │ │ │ └── Currying.lagda.md │ │ ├── Pointed.lagda.md │ │ └── Sigma.lagda.md │ ├── Underlying.agda │ ├── Univalence.lagda.md │ ├── Univalence │ │ ├── Fibrewise.lagda.md │ │ ├── SIP.lagda.md │ │ └── SIP │ │ │ └── Auto.agda │ └── intro.lagda.md ├── Algebra │ ├── Group.lagda.md │ ├── Group │ │ ├── Ab.lagda.md │ │ ├── Ab │ │ │ ├── Abelianisation.lagda.md │ │ │ ├── Free.lagda.md │ │ │ ├── Hom.lagda.md │ │ │ ├── Sum.lagda.md │ │ │ └── Tensor.lagda.md │ │ ├── Action.lagda.md │ │ ├── Cat │ │ │ ├── Base.lagda.md │ │ │ ├── FinitelyComplete.lagda.md │ │ │ └── Monadic.lagda.md │ │ ├── Cayley.lagda.md │ │ ├── Concrete.lagda.md │ │ ├── Concrete │ │ │ ├── Abelian.lagda.md │ │ │ ├── FinitelyComplete.lagda.md │ │ │ └── Semidirect.lagda.md │ │ ├── Free.lagda.md │ │ ├── Free │ │ │ ├── Product.lagda.md │ │ │ └── Words.lagda.md │ │ ├── Homotopy.lagda.md │ │ ├── Homotopy │ │ │ └── BAut.lagda.md │ │ ├── Instances │ │ │ ├── Cyclic.lagda.md │ │ │ ├── Dihedral.lagda.md │ │ │ ├── Integers.lagda.md │ │ │ └── Symmetric.lagda.md │ │ ├── NAry.lagda.md │ │ ├── Notation.agda │ │ ├── Semidirect.lagda.md │ │ ├── Solver.agda │ │ └── Subgroup.lagda.md │ ├── Magma.lagda.md │ ├── Magma │ │ ├── Unital.lagda.md │ │ └── Unital │ │ │ └── EckmannHilton.lagda.md │ ├── Monoid.lagda.md │ ├── Monoid │ │ ├── Category.lagda.md │ │ └── Reasoning.lagda.md │ ├── Quasigroup.lagda.md │ ├── Quasigroup │ │ └── Instances │ │ │ ├── Group.lagda.md │ │ │ └── Initial.lagda.md │ ├── Ring.lagda.md │ ├── Ring │ │ ├── Cat │ │ │ └── Initial.lagda.md │ │ ├── Commutative.lagda.md │ │ ├── Ideal.lagda.md │ │ ├── Localisation.lagda.md │ │ ├── Module.lagda.md │ │ ├── Module │ │ │ ├── Action.lagda.md │ │ │ ├── Category.lagda.md │ │ │ ├── Free.lagda.md │ │ │ ├── Multilinear.lagda.md │ │ │ ├── Notation.agda │ │ │ └── Vec.lagda.md │ │ ├── Quotient.lagda.md │ │ ├── Reasoning.lagda.md │ │ └── Solver.agda │ └── Semigroup.lagda.md ├── Borceux.lagda.md ├── Cat │ ├── Abelian │ │ ├── Base.lagda.md │ │ ├── Endo.lagda.md │ │ ├── Functor.lagda.md │ │ ├── Images.lagda.md │ │ ├── Instances │ │ │ ├── Ab.lagda.md │ │ │ └── Functor.lagda.md │ │ ├── Limits.lagda.md │ │ └── NAry.lagda.md │ ├── Allegory │ │ ├── Base.lagda.md │ │ ├── Instances │ │ │ └── Mat.lagda.md │ │ ├── Maps.lagda.md │ │ ├── Morphism.lagda.md │ │ └── Reasoning.lagda.md │ ├── Base.lagda.md │ ├── Bi │ │ ├── Base.lagda.md │ │ ├── Diagram │ │ │ ├── Adjunction.lagda.md │ │ │ ├── Monad.lagda.md │ │ │ └── Monad │ │ │ │ └── Spans.lagda.md │ │ └── Instances │ │ │ ├── Discrete.lagda.md │ │ │ ├── Displayed.lagda.md │ │ │ ├── InternalCats.lagda.md │ │ │ ├── Relations.lagda.md │ │ │ ├── Spans.lagda.md │ │ │ └── Terminal.lagda.md │ ├── Cartesian.lagda.md │ ├── CartesianClosed │ │ ├── Cont.lagda.md │ │ ├── Free.lagda.md │ │ ├── Free │ │ │ ├── Lambda.lagda.md │ │ │ └── Signature.lagda.md │ │ ├── Locally.lagda.md │ │ └── Solver.lagda.md │ ├── Connected.lagda.md │ ├── Diagram │ │ ├── Biproduct.lagda.md │ │ ├── Coend.lagda.md │ │ ├── Coend │ │ │ ├── Formula.lagda.md │ │ │ └── Sets.lagda.md │ │ ├── Coequaliser.lagda.md │ │ ├── Coequaliser │ │ │ └── RegularEpi.lagda.md │ │ ├── Colimit │ │ │ ├── Base.lagda.md │ │ │ ├── Cocone.lagda.md │ │ │ ├── Coequaliser.lagda.md │ │ │ ├── Coproduct.lagda.md │ │ │ ├── Finite.lagda.md │ │ │ ├── Initial.lagda.md │ │ │ ├── Representable.lagda.md │ │ │ ├── Terminal.lagda.md │ │ │ └── Universal.lagda.md │ │ ├── Comonad.lagda.md │ │ ├── Comonad │ │ │ └── Writer.lagda.md │ │ ├── Congruence.lagda.md │ │ ├── Coproduct.lagda.md │ │ ├── Coproduct │ │ │ ├── Copower.lagda.md │ │ │ └── Indexed.lagda.md │ │ ├── Coseparator.lagda.md │ │ ├── Duals.lagda.md │ │ ├── Equaliser.lagda.md │ │ ├── Equaliser │ │ │ ├── Joint.lagda.md │ │ │ ├── Kernel.lagda.md │ │ │ └── RegularMono.lagda.md │ │ ├── Exponential.lagda.md │ │ ├── Idempotent.lagda.md │ │ ├── Image.lagda.md │ │ ├── Initial.lagda.md │ │ ├── Initial │ │ │ ├── Strict.lagda.md │ │ │ └── Weak.lagda.md │ │ ├── Injective.lagda.md │ │ ├── Limit │ │ │ ├── Base.lagda.md │ │ │ ├── Cone.lagda.md │ │ │ ├── Equaliser.lagda.md │ │ │ ├── Finite.lagda.md │ │ │ ├── Initial.lagda.md │ │ │ ├── Product.lagda.md │ │ │ ├── Pullback.lagda.md │ │ │ └── Terminal.lagda.md │ │ ├── Monad.lagda.md │ │ ├── Monad │ │ │ ├── Action.lagda.md │ │ │ ├── Codensity.lagda.md │ │ │ ├── Extension.lagda.md │ │ │ ├── Idempotent.lagda.md │ │ │ ├── Kleisli.lagda.md │ │ │ ├── Relative.lagda.md │ │ │ └── Solver.agda │ │ ├── Omega.lagda.md │ │ ├── Product.lagda.md │ │ ├── Product │ │ │ ├── Finite.lagda.md │ │ │ ├── Indexed.lagda.md │ │ │ ├── Power.lagda.md │ │ │ └── Solver.lagda.md │ │ ├── Projective.lagda.md │ │ ├── Projective │ │ │ └── Strong.lagda.md │ │ ├── Pullback.lagda.md │ │ ├── Pullback │ │ │ ├── Along.lagda.md │ │ │ └── Properties.lagda.md │ │ ├── Pushout.lagda.md │ │ ├── Pushout │ │ │ └── Properties.lagda.md │ │ ├── Separator.lagda.md │ │ ├── Separator │ │ │ ├── Regular.lagda.md │ │ │ └── Strong.lagda.md │ │ ├── Sieve.lagda.md │ │ ├── Subterminal.lagda.md │ │ ├── Terminal.lagda.md │ │ └── Zero.lagda.md │ ├── Displayed │ │ ├── Adjoint.lagda.md │ │ ├── Base.lagda.md │ │ ├── BeckChevalley.lagda.md │ │ ├── Bifibration.lagda.md │ │ ├── Cartesian.lagda.md │ │ ├── Cartesian │ │ │ ├── Discrete.lagda.md │ │ │ ├── Identity.lagda.md │ │ │ ├── Indexing.lagda.md │ │ │ ├── Joint.lagda.md │ │ │ ├── Right.lagda.md │ │ │ ├── Street.lagda.md │ │ │ └── Weak.lagda.md │ │ ├── Cocartesian.lagda.md │ │ ├── Cocartesian │ │ │ ├── Discrete.lagda.md │ │ │ ├── Indexing.lagda.md │ │ │ └── Weak.lagda.md │ │ ├── Composition.lagda.md │ │ ├── Comprehension.lagda.md │ │ ├── Comprehension │ │ │ ├── Coproduct.lagda.md │ │ │ └── Coproduct │ │ │ │ ├── Strong.lagda.md │ │ │ │ └── VeryStrong.lagda.md │ │ ├── Diagram │ │ │ └── Total │ │ │ │ ├── Exponential.lagda.md │ │ │ │ ├── Product.lagda.md │ │ │ │ └── Terminal.lagda.md │ │ ├── Doctrine.lagda.md │ │ ├── Doctrine │ │ │ ├── Frame.lagda.md │ │ │ └── Logic.lagda.md │ │ ├── Fibre.lagda.md │ │ ├── Fibre │ │ │ └── Reasoning.lagda.md │ │ ├── Functor.lagda.md │ │ ├── GenericObject.lagda.md │ │ ├── Instances │ │ │ ├── CT-Structure.lagda.md │ │ │ ├── Chaotic.lagda.md │ │ │ ├── Comma.lagda.md │ │ │ ├── Diagrams.lagda.md │ │ │ ├── DisplayedFamilies.lagda.md │ │ │ ├── Elements.lagda.md │ │ │ ├── Externalisation.lagda.md │ │ │ ├── Family.lagda.md │ │ │ ├── Family │ │ │ │ └── Properties.lagda.md │ │ │ ├── Gluing.lagda.md │ │ │ ├── Identity.lagda.md │ │ │ ├── Lifting.lagda.md │ │ │ ├── Objects.lagda.md │ │ │ ├── Opposite.lagda.md │ │ │ ├── Pullback.lagda.md │ │ │ ├── Scone.lagda.md │ │ │ ├── Simple.lagda.md │ │ │ ├── Simple │ │ │ │ └── Properties.lagda.md │ │ │ ├── Slice.lagda.md │ │ │ ├── Slice │ │ │ │ ├── Comprehension.lagda.md │ │ │ │ └── Properties.lagda.md │ │ │ ├── Subobjects.lagda.md │ │ │ ├── Subobjects │ │ │ │ └── Reasoning.lagda.md │ │ │ ├── TotalProduct.lagda.md │ │ │ └── Trivial.lagda.md │ │ ├── InternalSum.lagda.md │ │ ├── Morphism.lagda.md │ │ ├── Morphism │ │ │ └── Duality.lagda.md │ │ ├── Path.lagda.md │ │ ├── Reasoning.lagda.md │ │ ├── Section.lagda.md │ │ ├── Solver.agda │ │ ├── Total.lagda.md │ │ ├── Total │ │ │ └── Op.lagda.md │ │ ├── TwoSided.lagda.md │ │ ├── TwoSided │ │ │ └── Discrete.lagda.md │ │ ├── Univalence.lagda.md │ │ └── Univalence │ │ │ ├── Reasoning.lagda.md │ │ │ └── Thin.lagda.md │ ├── Finite.lagda.md │ ├── Functor │ │ ├── Adjoint.lagda.md │ │ ├── Adjoint │ │ │ ├── AFT.lagda.md │ │ │ ├── Cofree.lagda.md │ │ │ ├── Colimit.lagda.md │ │ │ ├── Comonad.lagda.md │ │ │ ├── Comonadic.lagda.md │ │ │ ├── Compose.lagda.md │ │ │ ├── Conservative.lagda.md │ │ │ ├── ConstD.lagda.md │ │ │ ├── Continuous.lagda.md │ │ │ ├── Epireflective.lagda.md │ │ │ ├── Hom.lagda.md │ │ │ ├── Kan.lagda.md │ │ │ ├── Mate.lagda.md │ │ │ ├── Monad.lagda.md │ │ │ ├── Monadic.lagda.md │ │ │ ├── Properties.lagda.md │ │ │ ├── Reflective.lagda.md │ │ │ ├── Representable.lagda.md │ │ │ └── Unique.lagda.md │ │ ├── Algebra.lagda.md │ │ ├── Algebra │ │ │ ├── KnasterTarski.lagda.md │ │ │ └── Limits.lagda.md │ │ ├── Amnestic.lagda.md │ │ ├── Base.lagda.md │ │ ├── Bifunctor.lagda.md │ │ ├── Closed.lagda.md │ │ ├── Coherence.agda │ │ ├── Compose.lagda.md │ │ ├── Conservative.lagda.md │ │ ├── Constant.lagda.md │ │ ├── Dense.lagda.md │ │ ├── Equivalence.lagda.md │ │ ├── Equivalence │ │ │ ├── Path.lagda.md │ │ │ └── Properties.lagda.md │ │ ├── Final.lagda.md │ │ ├── FullSubcategory.lagda.md │ │ ├── Hom.lagda.md │ │ ├── Hom │ │ │ ├── Cocompletion.lagda.md │ │ │ ├── Coyoneda.lagda.md │ │ │ ├── Displayed.lagda.md │ │ │ ├── Duality.lagda.md │ │ │ ├── Properties.lagda.md │ │ │ ├── Representable.lagda.md │ │ │ └── Yoneda.lagda.md │ │ ├── Joint.lagda.md │ │ ├── Kan │ │ │ ├── Adjoint.lagda.md │ │ │ ├── Base.lagda.md │ │ │ ├── Duality.lagda.md │ │ │ ├── Global.lagda.md │ │ │ ├── Nerve.lagda.md │ │ │ ├── Pointwise.lagda.md │ │ │ ├── Reflection.agda │ │ │ ├── Representable.lagda.md │ │ │ └── Unique.lagda.md │ │ ├── Monadic │ │ │ ├── Beck.lagda.md │ │ │ └── Crude.lagda.md │ │ ├── Morphism.lagda.md │ │ ├── Naturality.lagda.md │ │ ├── Naturality │ │ │ └── Reflection.agda │ │ ├── Properties.lagda.md │ │ ├── Properties │ │ │ └── FullyFaithful.lagda.md │ │ ├── Pullback.lagda.md │ │ ├── Reasoning.lagda.md │ │ ├── Reasoning │ │ │ ├── FullyFaithful.lagda.md │ │ │ └── Presheaf.agda │ │ ├── Slice.lagda.md │ │ ├── Solver.agda │ │ ├── Subcategory.lagda.md │ │ ├── Univalence.lagda.md │ │ └── WideSubcategory.lagda.md │ ├── Gaunt.lagda.md │ ├── Groupoid.lagda.md │ ├── Instances │ │ ├── Algebras │ │ │ ├── Kan.lagda.md │ │ │ └── Limits.lagda.md │ │ ├── Assemblies.lagda.md │ │ ├── Assemblies │ │ │ ├── Colimits.lagda.md │ │ │ ├── Exponentials.lagda.md │ │ │ ├── Limits.lagda.md │ │ │ └── Univalence.lagda.md │ │ ├── Coalgebras.lagda.md │ │ ├── Coalgebras │ │ │ ├── Cartesian.lagda.md │ │ │ ├── Colimits.lagda.md │ │ │ └── Limits.lagda.md │ │ ├── Comma.lagda.md │ │ ├── Comma │ │ │ ├── Limits.lagda.md │ │ │ └── Univalent.lagda.md │ │ ├── Congruence.lagda.md │ │ ├── Core.lagda.md │ │ ├── Delooping.lagda.md │ │ ├── Discrete.lagda.md │ │ ├── Discrete │ │ │ └── Pre.lagda.md │ │ ├── Elements.lagda.md │ │ ├── Elements │ │ │ ├── Covariant.lagda.md │ │ │ └── Properties.lagda.md │ │ ├── FinSets.lagda.md │ │ ├── FinSets │ │ │ └── Omega.lagda.md │ │ ├── Free.lagda.md │ │ ├── Functor.lagda.md │ │ ├── Functor │ │ │ ├── Duality.lagda.md │ │ │ └── Limits.lagda.md │ │ ├── Graphs.lagda.md │ │ ├── Graphs │ │ │ ├── Box.lagda.md │ │ │ ├── Exponentials.lagda.md │ │ │ ├── Lift.lagda.md │ │ │ ├── Limits.lagda.md │ │ │ ├── Omega.lagda.md │ │ │ └── Representable.lagda.md │ │ ├── InternalFunctor.lagda.md │ │ ├── InternalFunctor │ │ │ └── Compose.lagda.md │ │ ├── Karoubi.lagda.md │ │ ├── Lift.lagda.md │ │ ├── Localisation.lagda.md │ │ ├── MarkedGraphs.lagda.md │ │ ├── Monads.lagda.md │ │ ├── OFE.lagda.md │ │ ├── OFE │ │ │ ├── Closed.lagda.md │ │ │ ├── Complete.lagda.md │ │ │ ├── Coproduct.lagda.md │ │ │ ├── Discrete.lagda.md │ │ │ ├── Later.lagda.md │ │ │ └── Product.lagda.md │ │ ├── OuterFunctor.lagda.md │ │ ├── Poly.lagda.md │ │ ├── Presheaf │ │ │ ├── Colimits.lagda.md │ │ │ ├── Exponentials.lagda.md │ │ │ ├── Limits.lagda.md │ │ │ └── Omega.lagda.md │ │ ├── Product.lagda.md │ │ ├── Sets.lagda.md │ │ ├── Sets │ │ │ ├── CartesianClosed.lagda.md │ │ │ ├── Cocomplete.lagda.md │ │ │ ├── Complete.lagda.md │ │ │ ├── Congruences.lagda.md │ │ │ └── Counterexamples │ │ │ │ └── SelfDual.lagda.md │ │ ├── Shape │ │ │ ├── Cospan.lagda.md │ │ │ ├── Initial.lagda.md │ │ │ ├── Interval.lagda.md │ │ │ ├── Involution.lagda.md │ │ │ ├── Isomorphism.lagda.md │ │ │ ├── Join.lagda.md │ │ │ ├── Parallel.lagda.md │ │ │ ├── Terminal.lagda.md │ │ │ ├── Terminal │ │ │ │ └── Properties.lagda.md │ │ │ └── Two.lagda.md │ │ ├── Sheaf │ │ │ ├── Exponentials.lagda.md │ │ │ ├── Limits.lagda.md │ │ │ ├── Limits │ │ │ │ └── Finite.lagda.md │ │ │ └── Omega.lagda.md │ │ ├── Sheaves.lagda.md │ │ ├── Simplex.lagda.md │ │ ├── Slice.lagda.md │ │ ├── Slice │ │ │ ├── Colimit.lagda.md │ │ │ ├── Limit.lagda.md │ │ │ ├── Presheaf.lagda.md │ │ │ └── Twice.lagda.md │ │ ├── StrictCat.lagda.md │ │ ├── StrictCat │ │ │ └── Cohesive.lagda.md │ │ └── Twisted.lagda.md │ ├── Internal │ │ ├── Base.lagda.md │ │ ├── Functor │ │ │ └── Outer.lagda.md │ │ ├── Instances │ │ │ ├── Congruence.lagda.md │ │ │ └── Discrete.lagda.md │ │ ├── Morphism.lagda.md │ │ ├── Opposite.lagda.md │ │ ├── Reasoning.lagda.md │ │ └── Sets.lagda.md │ ├── LocallyGraded │ │ └── Base.lagda.md │ ├── Monoidal │ │ ├── Base.lagda.md │ │ ├── Braided.lagda.md │ │ ├── Diagonals.lagda.md │ │ ├── Diagram │ │ │ ├── Monoid.lagda.md │ │ │ └── Monoid │ │ │ │ └── Representable.lagda.md │ │ ├── Functor.lagda.md │ │ ├── Instances │ │ │ ├── Cartesian.lagda.md │ │ │ └── Day.lagda.md │ │ ├── Monad.lagda.md │ │ ├── Reverse.lagda.md │ │ ├── Strength.lagda.md │ │ └── Strength │ │ │ └── Monad.lagda.md │ ├── Morphism.lagda.md │ ├── Morphism │ │ ├── Class.lagda.md │ │ ├── Duality.lagda.md │ │ ├── Factorisation.lagda.md │ │ ├── Factorisation │ │ │ └── Orthogonal.lagda.md │ │ ├── Instances.agda │ │ ├── Joint │ │ │ └── Mono.lagda.md │ │ ├── Lifts.lagda.md │ │ ├── Orthogonal.lagda.md │ │ └── Strong │ │ │ ├── Epi.lagda.md │ │ │ └── Mono.lagda.md │ ├── Natural │ │ └── Reasoning.lagda.md │ ├── Prelude.agda │ ├── Reasoning.lagda.md │ ├── Regular.lagda.md │ ├── Regular │ │ ├── Image.lagda.md │ │ ├── Instances │ │ │ └── Sets.lagda.md │ │ └── Slice.lagda.md │ ├── Restriction │ │ ├── Base.lagda.md │ │ ├── Functor.lagda.md │ │ ├── Instances │ │ │ └── Allegory.lagda.md │ │ ├── Reasoning.lagda.md │ │ └── Total.lagda.md │ ├── Site │ │ ├── Base.lagda.md │ │ ├── Closure.lagda.md │ │ ├── Constructions.lagda.md │ │ ├── Grothendieck.lagda.md │ │ ├── Instances │ │ │ ├── Atomic.lagda.md │ │ │ ├── Canonical.lagda.md │ │ │ └── Frame.lagda.md │ │ └── Sheafification.lagda.md │ ├── Skeletal.lagda.md │ ├── Solver.lagda.md │ ├── Strict.lagda.md │ ├── Strict │ │ └── Reasoning.lagda.md │ ├── Total.lagda.md │ ├── Total │ │ └── Instances │ │ │ ├── Reflective.lagda.md │ │ │ └── Set.lagda.md │ ├── Univalent.lagda.md │ └── Univalent │ │ ├── Instances │ │ └── Opposite.lagda.md │ │ ├── Rezk.lagda.md │ │ └── Rezk │ │ ├── HIT.lagda.md │ │ └── Universal.lagda.md ├── Data │ ├── Bool.lagda.md │ ├── Bool │ │ ├── Base.lagda.md │ │ └── Order.lagda.md │ ├── Char │ │ └── Base.lagda.md │ ├── Dec.lagda.md │ ├── Dec │ │ ├── Base.lagda.md │ │ └── Path.lagda.md │ ├── Fin.lagda.md │ ├── Fin │ │ ├── Base.lagda.md │ │ ├── CaseBash.lagda.md │ │ ├── Closure.lagda.md │ │ ├── Finite.lagda.md │ │ ├── Indexed.lagda.md │ │ ├── Product.lagda.md │ │ └── Properties.lagda.md │ ├── Finset │ │ ├── Base.lagda.md │ │ └── Properties.agda │ ├── Float │ │ └── Base.lagda.md │ ├── Id │ │ ├── Base.lagda.md │ │ └── Properties.agda │ ├── Image.lagda.md │ ├── Int.lagda.md │ ├── Int │ │ ├── Base.lagda.md │ │ ├── DivMod.lagda.md │ │ ├── Divisible.lagda.md │ │ ├── HIT.lagda.md │ │ ├── Order.lagda.md │ │ ├── Properties.lagda.md │ │ └── Universal.lagda.md │ ├── Irr.lagda.md │ ├── List.lagda.md │ ├── List │ │ ├── Base.lagda.md │ │ ├── Membership.lagda.md │ │ ├── NonEmpty.lagda.md │ │ ├── Pi.agda │ │ ├── Properties.lagda.md │ │ ├── Quantifiers.lagda.md │ │ └── Sigma.agda │ ├── Maybe.lagda.md │ ├── Maybe │ │ ├── Base.lagda.md │ │ └── Properties.lagda.md │ ├── Nat.lagda.md │ ├── Nat │ │ ├── Base.lagda.md │ │ ├── DivMod.lagda.md │ │ ├── Divisible.lagda.md │ │ ├── Divisible │ │ │ └── GCD.lagda.md │ │ ├── Order.lagda.md │ │ ├── Prime.lagda.md │ │ ├── Properties.lagda.md │ │ ├── Range.lagda.md │ │ └── Solver.lagda.md │ ├── Partial │ │ ├── Base.lagda.md │ │ ├── Properties.lagda.md │ │ └── Total.lagda.md │ ├── Power.lagda.md │ ├── Power │ │ └── Complemented.lagda.md │ ├── Product │ │ └── NAry.lagda.md │ ├── Rational │ │ ├── Base.lagda.md │ │ ├── Order.lagda.md │ │ ├── Properties.lagda.md │ │ ├── Reflection.agda │ │ └── Solver.agda │ ├── Reflection │ │ ├── Abs.agda │ │ ├── Argument.agda │ │ ├── Error.agda │ │ ├── Fixity.agda │ │ ├── Literal.agda │ │ ├── Meta.agda │ │ ├── Name.agda │ │ └── Term.agda │ ├── Set │ │ ├── Coequaliser.lagda.md │ │ ├── Coequaliser │ │ │ └── Split.lagda.md │ │ ├── Material.lagda.md │ │ ├── Material │ │ │ ├── Automation.lagda.md │ │ │ └── HIT.lagda.md │ │ ├── Projective.lagda.md │ │ ├── Pushout.lagda.md │ │ ├── Surjection.lagda.md │ │ └── Truncation.lagda.md │ ├── String │ │ ├── Base.lagda.md │ │ └── Show.lagda.md │ ├── Sum.lagda.md │ ├── Sum │ │ ├── Base.lagda.md │ │ └── Properties.lagda.md │ ├── Vec │ │ ├── Base.lagda.md │ │ └── Properties.lagda.md │ ├── Wellfounded │ │ ├── Base.lagda.md │ │ ├── Properties.lagda.md │ │ └── W.lagda.md │ └── Word │ │ └── Base.lagda.md ├── Elephant.lagda.md ├── HoTT.lagda.md ├── Homotopy │ ├── Base.lagda.md │ ├── Conjugation.lagda.md │ ├── Connectedness.lagda.md │ ├── Connectedness │ │ └── Automation.lagda.md │ ├── HSpace.lagda.md │ ├── Join.lagda.md │ ├── Loopspace.lagda.md │ ├── Pushout.lagda.md │ ├── Space │ │ ├── Circle.agda │ │ ├── Circle │ │ │ ├── Base.lagda.md │ │ │ └── Properties.lagda.md │ │ ├── Delooping.lagda.md │ │ ├── Rose.lagda.md │ │ ├── Sinfty.lagda.md │ │ ├── Sphere.lagda.md │ │ ├── Sphere │ │ │ ├── Degree.lagda.md │ │ │ └── Properties.lagda.md │ │ ├── Suspension.lagda.md │ │ ├── Suspension │ │ │ ├── Freudenthal.lagda.md │ │ │ ├── Pi2.lagda.md │ │ │ └── Properties.lagda.md │ │ └── Torus.lagda.md │ ├── Truncation.lagda.md │ └── Wedge.lagda.md ├── Logic │ └── Propositional │ │ ├── Classical.lagda.md │ │ └── Classical │ │ ├── CNF.lagda.md │ │ ├── Compactness.lagda.md │ │ └── SAT.lagda.md ├── Meta │ ├── Alt.lagda.md │ ├── Append.lagda.md │ ├── Bind.lagda.md │ ├── Brackets.lagda.md │ ├── Foldable.lagda.md │ ├── Idiom.lagda.md │ ├── Invariant.lagda.md │ └── Traversable.lagda.md ├── Order │ ├── Base.lagda.md │ ├── Cat.lagda.md │ ├── DCPO.lagda.md │ ├── DCPO │ │ ├── Free.lagda.md │ │ └── Pointed.lagda.md │ ├── Diagram │ │ ├── Bottom.lagda.md │ │ ├── Fixpoint.lagda.md │ │ ├── Glb.lagda.md │ │ ├── Glb │ │ │ └── Reasoning.lagda.md │ │ ├── Join.lagda.md │ │ ├── Join │ │ │ └── Reasoning.lagda.md │ │ ├── Lub.lagda.md │ │ ├── Lub │ │ │ ├── Reasoning.lagda.md │ │ │ └── Subset.lagda.md │ │ ├── Meet.lagda.md │ │ ├── Meet │ │ │ └── Reasoning.lagda.md │ │ └── Top.lagda.md │ ├── Displayed.lagda.md │ ├── Frame.lagda.md │ ├── Frame │ │ ├── Free.lagda.md │ │ └── Reasoning.lagda.md │ ├── Heyting.lagda.md │ ├── Instances │ │ ├── Coproduct.lagda.md │ │ ├── Discrete.lagda.md │ │ ├── Disjoint.lagda.md │ │ ├── Int.lagda.md │ │ ├── LexicalSum.lagda.md │ │ ├── Lift.lagda.md │ │ ├── Lower.lagda.md │ │ ├── Lower │ │ │ └── Cocompletion.lagda.md │ │ ├── Nat.lagda.md │ │ ├── Pointwise.lagda.md │ │ ├── Pointwise │ │ │ └── Diagrams.lagda.md │ │ ├── Product.lagda.md │ │ ├── Props.lagda.md │ │ └── Rational.lagda.md │ ├── Lattice.lagda.md │ ├── Lattice │ │ ├── Distributive.lagda.md │ │ └── Reasoning.lagda.md │ ├── Morphism.lagda.md │ ├── Reasoning.lagda.md │ ├── Semilattice │ │ ├── Free.lagda.md │ │ ├── Join.lagda.md │ │ ├── Join │ │ │ ├── NAry.lagda.md │ │ │ ├── Reasoning.lagda.md │ │ │ └── Subsemilattice.lagda.md │ │ ├── Meet.lagda.md │ │ └── Meet │ │ │ ├── NAry.lagda.md │ │ │ └── Reasoning.lagda.md │ ├── Subposet.lagda.md │ ├── Total.lagda.md │ └── Univalent.lagda.md ├── Prim │ ├── Data │ │ ├── Bool.lagda.md │ │ ├── Nat.lagda.md │ │ └── Sigma.lagda.md │ ├── Extension.lagda.md │ ├── HCompU.lagda.md │ ├── Interval.lagda.md │ ├── Kan.lagda.md │ ├── Literals.lagda.md │ └── Type.lagda.md ├── Realisability │ ├── Base.lagda.md │ ├── Data │ │ ├── Bool.lagda.md │ │ ├── Nat.lagda.md │ │ ├── Pair.lagda.md │ │ └── Sum.lagda.md │ ├── PCA.lagda.md │ └── PCA │ │ ├── Combinatorial.lagda.md │ │ ├── Fixpoint.lagda.md │ │ ├── Instances │ │ └── Free.lagda.md │ │ ├── Sugar.lagda.md │ │ └── Trivial.lagda.md ├── Talks │ └── Topos2024.lagda.md ├── Topoi │ ├── Base.lagda.md │ ├── Classifying │ │ └── Diaconescu.lagda.md │ └── Reasoning.lagda.md ├── bibliography.bibtex ├── index.lagda.md └── preamble.tex ├── support ├── check.sh ├── diagram.tex ├── everything.sh ├── favicon.ico ├── katex │ └── katex-worker.js ├── make-site.sh ├── nix │ ├── build-shake.nix │ ├── dep │ │ ├── Agda │ │ │ ├── default.nix │ │ │ ├── github.json │ │ │ └── thunk.nix │ │ └── nix-thunk │ │ │ ├── default.nix │ │ │ ├── github.json │ │ │ └── thunk.nix │ ├── haskell-packages.nix │ ├── nixpkgs.nix │ └── node │ │ ├── node-dependencies.nix │ │ └── node-env.nix ├── shake │ ├── .gitignore │ ├── 1lab-shake.cabal │ ├── CHANGELOG.md │ ├── LICENSE.agda │ ├── README.md │ └── app │ │ ├── Agda.hs │ │ ├── Definitions.hs │ │ ├── HTML │ │ ├── Backend.hs │ │ ├── Base.hs │ │ └── Render.hs │ │ ├── Macros.hs │ │ ├── Main.hs │ │ ├── Shake │ │ ├── AgdaCompile.hs │ │ ├── Diagram.hs │ │ ├── Digest.hs │ │ ├── Git.hs │ │ ├── Highlights.hs │ │ ├── KaTeX.hs │ │ ├── LinkGraph.hs │ │ ├── LinkReferences.hs │ │ ├── Markdown.hs │ │ ├── Markdown │ │ │ └── Reader.hs │ │ ├── Modules.hs │ │ ├── Options.hs │ │ ├── Recent.hs │ │ ├── SearchData.hs │ │ └── Utils.hs │ │ └── Timer.hs ├── sort-imports.hs ├── static │ ├── cube-128x.png │ ├── cube-32x.png │ ├── cube-512x.png │ ├── cube-72x.png │ ├── icons │ │ ├── all-pages.svg │ │ ├── github.svg │ │ ├── home.svg │ │ ├── justified.svg │ │ ├── raggedleft.svg │ │ ├── raggedright.svg │ │ ├── serif.svg │ │ ├── star.svg │ │ └── view-controls.svg │ ├── licenses │ │ ├── LICENSE.EBGaramond.txt │ │ ├── LICENSE.InriaSans.txt │ │ ├── LICENSE.JuliaMono.txt │ │ ├── LICENSE.KaTeX.txt │ │ ├── LICENSE.Noto.txt │ │ ├── LICENSE.Octicons.txt │ │ └── LICENSE.fast-fuzzy.txt │ ├── lies-over-dark.svg │ └── lies-over-light.svg └── web │ ├── css │ ├── code.scss │ ├── colors.scss │ ├── components │ │ ├── comments.scss │ │ ├── commit.scss │ │ ├── controls.scss │ │ ├── modal.scss │ │ ├── popup.scss │ │ ├── search.scss │ │ ├── sidenotes.scss │ │ └── toc.scss │ ├── default.scss │ ├── mixins.scss │ ├── talk.scss │ ├── theme.scss │ └── vars.scss │ ├── highlights │ ├── note.svg │ ├── source.svg │ ├── terminology.svg │ └── warning.svg │ ├── js │ ├── code-only.ts │ ├── equations.ts │ ├── highlight-hover.ts │ ├── lib │ │ ├── external.d.ts │ │ ├── hover.ts │ │ ├── jsx.ts │ │ ├── settings.tsx │ │ └── timeout.ts │ ├── main.ts │ ├── prompt.tsx │ ├── prompt │ │ ├── items.tsx │ │ └── sections.tsx │ ├── search.tsx │ ├── sidebar.tsx │ ├── sidenotes.tsx │ ├── start.ts │ └── theme.tsx │ ├── template.html │ └── template.reveal.html └── tsconfig.json /.editorconfig: 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