Agda.Builtin.Bool
Compiler support
Chapters 1 and 2 use the rebuild2 formalization. Agda links for Chapter 3 remain temporarily unavailable.
The checked modules supporting these sections are accessible here.
Modules
Agda.Builtin.Nat
Compiler support
Agda.Primitive
Compiler support
Calculus.Composition
SCT.Calculus.Composition
Checked aggregate · Source file
Calculus.Pasting
SCT.Calculus.Pasting
Checked aggregate · Source file
Calculus.Squares
SCT.Calculus.Squares
Checked aggregate · Source file
WebEdition
SCT.WebEdition
Checked aggregate · Source file
Chapter 1: The language of synthetic category theory
1.1 The basic vocabulary
Terminal
SCT.VolumeI.Chapter01.Section01.Terminal
Terms
SCT.VolumeI.Chapter01.Section01.Terms
Vocabulary
SCT.VolumeI.Chapter01.Section01.Vocabulary
1.2 Coherences
Coherence
SCT.VolumeI.Chapter01.Section02.Coherence
HorizontalComposition
SCT.VolumeI.Chapter01.Section02.HorizontalComposition
IdentificationSquares
SCT.VolumeI.Chapter01.Section02.IdentificationSquares
Naturality
SCT.VolumeI.Chapter01.Section02.Naturality
Products
SCT.VolumeI.Chapter01.Section02.Products
Specialization
SCT.VolumeI.Chapter01.Section02.Specialization
Whiskering
SCT.VolumeI.Chapter01.Section02.Whiskering
1.3 Equivalences of categories
Equivalences
SCT.VolumeI.Chapter01.Section03.Equivalences
Factorizations
SCT.VolumeI.Chapter01.Section03.Factorizations
ProductConstructions
SCT.VolumeI.Chapter01.Section03.ProductConstructions
RelativeFunctors
SCT.VolumeI.Chapter01.Section03.RelativeFunctors
RetractLoops
SCT.VolumeI.Chapter01.Section03.RetractLoops
Retracts
SCT.VolumeI.Chapter01.Section03.Retracts
Squares
SCT.VolumeI.Chapter01.Section03.Squares
Supporting
SCT.VolumeI.Chapter01.Section03.Supporting
WhiskeringEquivalence
SCT.VolumeI.Chapter01.Section03.WhiskeringEquivalence
Identifications
EndpointTransport
SCT.VolumeI.Chapter01.Section03.Identifications.EndpointTransport
FunctorCoherence
SCT.VolumeI.Chapter01.Section03.Identifications.FunctorCoherence
IdentificationSquares
SCT.VolumeI.Chapter01.Section03.Identifications.IdentificationSquares
Inverses
SCT.VolumeI.Chapter01.Section03.Identifications.Inverses
OverBase
SCT.VolumeI.Chapter01.Section03.Identifications.OverBase
ProjectedFactorization
SCT.VolumeI.Chapter01.Section03.Identifications.ProjectedFactorization
RestrictionDiagrams
SCT.VolumeI.Chapter01.Section03.Identifications.RestrictionDiagrams
RetractionCoherence
SCT.VolumeI.Chapter01.Section03.Identifications.RetractionCoherence
SectionEvaluation
SCT.VolumeI.Chapter01.Section03.Identifications.SectionEvaluation
TriangleCoherence
SCT.VolumeI.Chapter01.Section03.Identifications.TriangleCoherence
Triangles
SCT.VolumeI.Chapter01.Section03.Identifications.Triangles
Products
BinaryFunctors
SCT.VolumeI.Chapter01.Section03.Products.BinaryFunctors
Equivalences
SCT.VolumeI.Chapter01.Section03.Products.Equivalences
FirstFactorSubstitution
SCT.VolumeI.Chapter01.Section03.Products.FirstFactorSubstitution
PairedVertexFrames
SCT.VolumeI.Chapter01.Section03.Products.PairedVertexFrames
Pairing
SCT.VolumeI.Chapter01.Section03.Products.Pairing
PairingOverBase
SCT.VolumeI.Chapter01.Section03.Products.PairingOverBase
PairingRestriction
SCT.VolumeI.Chapter01.Section03.Products.PairingRestriction
PairingSquares
SCT.VolumeI.Chapter01.Section03.Products.PairingSquares
ProductFunctor
SCT.VolumeI.Chapter01.Section03.Products.ProductFunctor
ProductFunctorCoherence
SCT.VolumeI.Chapter01.Section03.Products.ProductFunctorCoherence
ProductPairing
SCT.VolumeI.Chapter01.Section03.Products.ProductPairing
ProductPairingComposition
SCT.VolumeI.Chapter01.Section03.Products.ProductPairingComposition
ProductPairingIdentity
SCT.VolumeI.Chapter01.Section03.Products.ProductPairingIdentity
ProductRestriction
SCT.VolumeI.Chapter01.Section03.Products.ProductRestriction
TripleEvaluationOuterImage
SCT.VolumeI.Chapter01.Section03.Products.TripleEvaluationOuterImage
1.4 Mapping animae
Coherence
SCT.VolumeI.Chapter01.Section04.Coherence
Composition
SCT.VolumeI.Chapter01.Section04.Composition
CompositionCoherence
SCT.VolumeI.Chapter01.Section04.CompositionCoherence
CompositionEvaluation
SCT.VolumeI.Chapter01.Section04.CompositionEvaluation
CompositionEvaluationFamily
SCT.VolumeI.Chapter01.Section04.CompositionEvaluationFamily
CompositionLawRestriction
SCT.VolumeI.Chapter01.Section04.CompositionLawRestriction
CompositionLaws
SCT.VolumeI.Chapter01.Section04.CompositionLaws
CompositionNaturality
SCT.VolumeI.Chapter01.Section04.CompositionNaturality
CompositionRestriction
SCT.VolumeI.Chapter01.Section04.CompositionRestriction
Core
SCT.VolumeI.Chapter01.Section04.Core
Currying
SCT.VolumeI.Chapter01.Section04.Currying
CurryingRestriction
SCT.VolumeI.Chapter01.Section04.CurryingRestriction
EquivalenceDetection
SCT.VolumeI.Chapter01.Section04.EquivalenceDetection
EvaluationCoherence
SCT.VolumeI.Chapter01.Section04.EvaluationCoherence
EvaluationOverBase
SCT.VolumeI.Chapter01.Section04.EvaluationOverBase
EvaluationRestriction
SCT.VolumeI.Chapter01.Section04.EvaluationRestriction
Functoriality
SCT.VolumeI.Chapter01.Section04.Functoriality
IdentityRestriction
SCT.VolumeI.Chapter01.Section04.IdentityRestriction
MappingAnimae
SCT.VolumeI.Chapter01.Section04.MappingAnimae
MappingProducts
SCT.VolumeI.Chapter01.Section04.MappingProducts
MappingSpecialization
SCT.VolumeI.Chapter01.Section04.MappingSpecialization
Points
SCT.VolumeI.Chapter01.Section04.Points
Precomposition
SCT.VolumeI.Chapter01.Section04.Precomposition
Uncurrying
SCT.VolumeI.Chapter01.Section04.Uncurrying
UncurryingRestriction
SCT.VolumeI.Chapter01.Section04.UncurryingRestriction
1.5 Initial categories and coproducts
Copairing
SCT.VolumeI.Chapter01.Section05.Copairing
CoproductConstructions
SCT.VolumeI.Chapter01.Section05.CoproductConstructions
Coproducts
SCT.VolumeI.Chapter01.Section05.Coproducts
IdentificationRestriction
SCT.VolumeI.Chapter01.Section05.IdentificationRestriction
Initial
SCT.VolumeI.Chapter01.Section05.Initial
1.6 Pullbacks of categories
ConeFramings
SCT.VolumeI.Chapter01.Section06.ConeFramings
ConeIdentifications
SCT.VolumeI.Chapter01.Section06.ConeIdentifications
ConePasting
SCT.VolumeI.Chapter01.Section06.ConePasting
ConeTransport
SCT.VolumeI.Chapter01.Section06.ConeTransport
ConeUniversality
SCT.VolumeI.Chapter01.Section06.ConeUniversality
Cones
SCT.VolumeI.Chapter01.Section06.Cones
CoproductDescent
SCT.VolumeI.Chapter01.Section06.CoproductDescent
DiagonalPullbacks
SCT.VolumeI.Chapter01.Section06.DiagonalPullbacks
DisjointCoproducts
SCT.VolumeI.Chapter01.Section06.DisjointCoproducts
Distributivity
SCT.VolumeI.Chapter01.Section06.Distributivity
EmbeddingCharacterizations
SCT.VolumeI.Chapter01.Section06.EmbeddingCharacterizations
Embeddings
SCT.VolumeI.Chapter01.Section06.Embeddings
MappingPullbacks
SCT.VolumeI.Chapter01.Section06.MappingPullbacks
NestedPullbacks
SCT.VolumeI.Chapter01.Section06.NestedPullbacks
PastingLemma
SCT.VolumeI.Chapter01.Section06.PastingLemma
PullbackArrowChange
SCT.VolumeI.Chapter01.Section06.PullbackArrowChange
PullbackAssociativity
SCT.VolumeI.Chapter01.Section06.PullbackAssociativity
PullbackCancellation
SCT.VolumeI.Chapter01.Section06.PullbackCancellation
PullbackConstructions
SCT.VolumeI.Chapter01.Section06.PullbackConstructions
PullbackFunctoriality
SCT.VolumeI.Chapter01.Section06.PullbackFunctoriality
PullbackSquares
SCT.VolumeI.Chapter01.Section06.PullbackSquares
PullbackTransfer
SCT.VolumeI.Chapter01.Section06.PullbackTransfer
Pullbacks
SCT.VolumeI.Chapter01.Section06.Pullbacks
Representability
SCT.VolumeI.Chapter01.Section06.Representability
RepresentabilityDiagonal
SCT.VolumeI.Chapter01.Section06.RepresentabilityDiagonal
SectionBaseChange
SCT.VolumeI.Chapter01.Section06.SectionBaseChange
UniversalConeIdentifications
SCT.VolumeI.Chapter01.Section06.UniversalConeIdentifications
UniversalCoproducts
SCT.VolumeI.Chapter01.Section06.UniversalCoproducts
1.7 Functor categories
CoproductDomain
SCT.VolumeI.Chapter01.Section07.CoproductDomain
CoreOfFun
SCT.VolumeI.Chapter01.Section07.CoreOfFun
Currying
SCT.VolumeI.Chapter01.Section07.Currying
Evaluation
SCT.VolumeI.Chapter01.Section07.Evaluation
EvaluationRepresentation
SCT.VolumeI.Chapter01.Section07.EvaluationRepresentation
EvaluationSubstitution
SCT.VolumeI.Chapter01.Section07.EvaluationSubstitution
ExponentialLaw
SCT.VolumeI.Chapter01.Section07.ExponentialLaw
FunctorCategories
SCT.VolumeI.Chapter01.Section07.FunctorCategories
FunctorConeRestriction
SCT.VolumeI.Chapter01.Section07.FunctorConeRestriction
FunctorCones
SCT.VolumeI.Chapter01.Section07.FunctorCones
FunctorProducts
SCT.VolumeI.Chapter01.Section07.FunctorProducts
FunctorProperties
SCT.VolumeI.Chapter01.Section07.FunctorProperties
FunctorPullbacks
SCT.VolumeI.Chapter01.Section07.FunctorPullbacks
Functoriality
SCT.VolumeI.Chapter01.Section07.Functoriality
InitialDomain
SCT.VolumeI.Chapter01.Section07.InitialDomain
PostEvaluationSubstitution
SCT.VolumeI.Chapter01.Section07.PostEvaluationSubstitution
PreEvaluationSubstitution
SCT.VolumeI.Chapter01.Section07.PreEvaluationSubstitution
1.8 Pushout squares
Cocones
SCT.VolumeI.Chapter01.Section08.Cocones
FunctorMappingOutEvaluation
SCT.VolumeI.Chapter01.Section08.FunctorMappingOutEvaluation
FunctorPushoutCriterion
SCT.VolumeI.Chapter01.Section08.FunctorPushoutCriterion
MappingOutEvaluation
SCT.VolumeI.Chapter01.Section08.MappingOutEvaluation
PushoutPasting
SCT.VolumeI.Chapter01.Section08.PushoutPasting
PushoutSquares
SCT.VolumeI.Chapter01.Section08.PushoutSquares
1.9 Categories over a base
NamedEvaluation
SCT.VolumeI.Chapter01.Section09.NamedEvaluation
RelativeBaseChange
SCT.VolumeI.Chapter01.Section09.RelativeBaseChange
RelativeFamilyComparisons
SCT.VolumeI.Chapter01.Section09.RelativeFamilyComparisons
RelativeFunctorCategories
SCT.VolumeI.Chapter01.Section09.RelativeFunctorCategories
RelativeInverseLaws
SCT.VolumeI.Chapter01.Section09.RelativeInverseLaws
RelativeMappingAnimae
SCT.VolumeI.Chapter01.Section09.RelativeMappingAnimae
RelativeProducts
SCT.VolumeI.Chapter01.Section09.RelativeProducts
RelativePullbackBaseChange
SCT.VolumeI.Chapter01.Section09.RelativePullbackBaseChange
RelativeTerminal
SCT.VolumeI.Chapter01.Section09.RelativeTerminal
Chapter 2: The internal structure of categories
2.1 Morphisms and diagrams
CoreCoproducts
SCT.VolumeI.Chapter02.Section01.CoreCoproducts
CoreInclusions
SCT.VolumeI.Chapter02.Section01.CoreInclusions
HomAndSlices
SCT.VolumeI.Chapter02.Section01.HomAndSlices
IdentityFamilyPostcomposition
SCT.VolumeI.Chapter02.Section01.IdentityFamilyPostcomposition
IdentityFamilyRestriction
SCT.VolumeI.Chapter02.Section01.IdentityFamilyRestriction
IdentityFamilyTransport
SCT.VolumeI.Chapter02.Section01.IdentityFamilyTransport
InsertionSectionComparison
SCT.VolumeI.Chapter02.Section01.InsertionSectionComparison
InsertionSectionEvaluation
SCT.VolumeI.Chapter02.Section01.InsertionSectionEvaluation
MorphismFamilyComparisons
SCT.VolumeI.Chapter02.Section01.MorphismFamilyComparisons
MorphismFamilyOperations
SCT.VolumeI.Chapter02.Section01.MorphismFamilyOperations
MorphismFamilyPostcomposition
SCT.VolumeI.Chapter02.Section01.MorphismFamilyPostcomposition
MorphismFamilyPostcompositionPasting
SCT.VolumeI.Chapter02.Section01.MorphismFamilyPostcompositionPasting
MorphismFamilyReflection
SCT.VolumeI.Chapter02.Section01.MorphismFamilyReflection
MorphismFraming
SCT.VolumeI.Chapter02.Section01.MorphismFraming
MorphismFunctor
SCT.VolumeI.Chapter02.Section01.MorphismFunctor
Morphisms
SCT.VolumeI.Chapter02.Section01.Morphisms
PointEvaluationAction
SCT.VolumeI.Chapter02.Section01.PointEvaluationAction
PointEvaluationComposition
SCT.VolumeI.Chapter02.Section01.PointEvaluationComposition
PointEvaluationCorners
SCT.VolumeI.Chapter02.Section01.PointEvaluationCorners
PointEvaluationIdentity
SCT.VolumeI.Chapter02.Section01.PointEvaluationIdentity
PointEvaluationParameters
SCT.VolumeI.Chapter02.Section01.PointEvaluationParameters
PointEvaluationPostcomposition
SCT.VolumeI.Chapter02.Section01.PointEvaluationPostcomposition
PointEvaluationShapes
SCT.VolumeI.Chapter02.Section01.PointEvaluationShapes
PostcompositionPointNaturality
SCT.VolumeI.Chapter02.Section01.PostcompositionPointNaturality
PostcompositionRestriction
SCT.VolumeI.Chapter02.Section01.PostcompositionRestriction
RepresentedDiagramPostcomposition
SCT.VolumeI.Chapter02.Section01.RepresentedDiagramPostcomposition
RestrictedDiagramEvaluation
SCT.VolumeI.Chapter02.Section01.RestrictedDiagramEvaluation
SliceFibers
SCT.VolumeI.Chapter02.Section01.SliceFibers
SquareGluing
SCT.VolumeI.Chapter02.Section01.SquareGluing
TriangleCore
SCT.VolumeI.Chapter02.Section01.TriangleCore
Triangles
SCT.VolumeI.Chapter02.Section01.Triangles
WalkingMorphism
SCT.VolumeI.Chapter02.Section01.WalkingMorphism
WalkingTriangle
SCT.VolumeI.Chapter02.Section01.WalkingTriangle
2.2 The Segal axiom
CommonDiagramDiagonal
SCT.VolumeI.Chapter02.Section02.CommonDiagramDiagonal
ConstantRestrictionEvaluation
SCT.VolumeI.Chapter02.Section02.ConstantRestrictionEvaluation
FixedInputMorphismFamilies
SCT.VolumeI.Chapter02.Section02.FixedInputMorphismFamilies
FramedCornerPostcomposition
SCT.VolumeI.Chapter02.Section02.FramedCornerPostcomposition
FramedDiagramTransport
SCT.VolumeI.Chapter02.Section02.FramedDiagramTransport
FramedSquareCommutativity
SCT.VolumeI.Chapter02.Section02.FramedSquareCommutativity
FramedSquares
SCT.VolumeI.Chapter02.Section02.FramedSquares
FramedTrianglePresentations
SCT.VolumeI.Chapter02.Section02.FramedTrianglePresentations
GluedFramedSquares
SCT.VolumeI.Chapter02.Section02.GluedFramedSquares
GluedTrianglePresentations
SCT.VolumeI.Chapter02.Section02.GluedTrianglePresentations
Interchange
SCT.VolumeI.Chapter02.Section02.Interchange
InternalComposition
SCT.VolumeI.Chapter02.Section02.InternalComposition
MorphismComposition
SCT.VolumeI.Chapter02.Section02.MorphismComposition
MorphismCompositionAssociativity
SCT.VolumeI.Chapter02.Section02.MorphismCompositionAssociativity
MorphismCompositionComparisons
SCT.VolumeI.Chapter02.Section02.MorphismCompositionComparisons
MorphismCompositionPostcomposition
SCT.VolumeI.Chapter02.Section02.MorphismCompositionPostcomposition
MorphismCompositionPresentation
SCT.VolumeI.Chapter02.Section02.MorphismCompositionPresentation
MorphismCompositionTransport
SCT.VolumeI.Chapter02.Section02.MorphismCompositionTransport
MorphismCompositionUnits
SCT.VolumeI.Chapter02.Section02.MorphismCompositionUnits
NaturalTransformationNaturality
SCT.VolumeI.Chapter02.Section02.NaturalTransformationNaturality
NaturalTransformationWhiskering
SCT.VolumeI.Chapter02.Section02.NaturalTransformationWhiskering
OriginalTriangleBoundaryComparisons
SCT.VolumeI.Chapter02.Section02.OriginalTriangleBoundaryComparisons
PostcompositionCorners
SCT.VolumeI.Chapter02.Section02.PostcompositionCorners
PrimitiveIdentificationComposition
SCT.VolumeI.Chapter02.Section02.PrimitiveIdentificationComposition
ProductInterchange
SCT.VolumeI.Chapter02.Section02.ProductInterchange
ProductMorphismFamilies
SCT.VolumeI.Chapter02.Section02.ProductMorphismFamilies
RecoveredVertexFrame
SCT.VolumeI.Chapter02.Section02.RecoveredVertexFrame
RelativeTriangleFraming
SCT.VolumeI.Chapter02.Section02.RelativeTriangleFraming
SegalAxiom
SCT.VolumeI.Chapter02.Section02.SegalAxiom
SegalComposition
SCT.VolumeI.Chapter02.Section02.SegalComposition
SquareBoundaryCones
SCT.VolumeI.Chapter02.Section02.SquareBoundaryCones
SquareCoordinates
SCT.VolumeI.Chapter02.Section02.SquareCoordinates
SquareCornerCompatibility
SCT.VolumeI.Chapter02.Section02.SquareCornerCompatibility
SquareCornerCoordinates
SCT.VolumeI.Chapter02.Section02.SquareCornerCoordinates
SquareCornerEndpoints
SCT.VolumeI.Chapter02.Section02.SquareCornerEndpoints
SquareCorners
SCT.VolumeI.Chapter02.Section02.SquareCorners
SquareCurrying
SCT.VolumeI.Chapter02.Section02.SquareCurrying
SquareVertexShapes
SCT.VolumeI.Chapter02.Section02.SquareVertexShapes
TriangleCompletionPresentation
SCT.VolumeI.Chapter02.Section02.TriangleCompletionPresentation
TriangleCornerFrames
SCT.VolumeI.Chapter02.Section02.TriangleCornerFrames
TriangleEndpointComparison
SCT.VolumeI.Chapter02.Section02.TriangleEndpointComparison
TriangleOuterFactorization
SCT.VolumeI.Chapter02.Section02.TriangleOuterFactorization
TriangleOuterFrames
SCT.VolumeI.Chapter02.Section02.TriangleOuterFrames
TrianglePresentationChange
SCT.VolumeI.Chapter02.Section02.TrianglePresentationChange
TrianglePresentationPostcomposition
SCT.VolumeI.Chapter02.Section02.TrianglePresentationPostcomposition
TrianglePullbacks
SCT.VolumeI.Chapter02.Section02.TrianglePullbacks
TriangleShortEdgeComparison
SCT.VolumeI.Chapter02.Section02.TriangleShortEdgeComparison
UnitPresentations
SCT.VolumeI.Chapter02.Section02.UnitPresentations
UnitTriangles
SCT.VolumeI.Chapter02.Section02.UnitTriangles
WholeCornerFramedSquares
SCT.VolumeI.Chapter02.Section02.WholeCornerFramedSquares
Square Calculus
EvaluationFrameTransport
SCT.VolumeI.Chapter02.Section02.SquareCalculus.EvaluationFrameTransport
ProductCoordinateFrames
SCT.VolumeI.Chapter02.Section02.SquareCalculus.ProductCoordinateFrames
TerminalSectionCoordinates
SCT.VolumeI.Chapter02.Section02.SquareCalculus.TerminalSectionCoordinates
2.3 The Rezk axiom
InverseMorphismFamilies
SCT.VolumeI.Chapter02.Section03.InverseMorphismFamilies
InvertibleMorphismFamilies
SCT.VolumeI.Chapter02.Section03.InvertibleMorphismFamilies
IsomorphismEmbedding
SCT.VolumeI.Chapter02.Section03.IsomorphismEmbedding
Isomorphisms
SCT.VolumeI.Chapter02.Section03.Isomorphisms
NaturalIsomorphisms
SCT.VolumeI.Chapter02.Section03.NaturalIsomorphisms
RezkAxiom
SCT.VolumeI.Chapter02.Section03.RezkAxiom
RezkFibers
SCT.VolumeI.Chapter02.Section03.RezkFibers
2.4 Groupoids
BasicClosure
SCT.VolumeI.Chapter02.Section04.BasicClosure
EvaluationCones
SCT.VolumeI.Chapter02.Section04.EvaluationCones
FunctorGroupoids
SCT.VolumeI.Chapter02.Section04.FunctorGroupoids
GroupoidCharacterization
SCT.VolumeI.Chapter02.Section04.GroupoidCharacterization
Groupoids
SCT.VolumeI.Chapter02.Section04.Groupoids
PullbackGroupoids
SCT.VolumeI.Chapter02.Section04.PullbackGroupoids
RetractGroupoids
SCT.VolumeI.Chapter02.Section04.RetractGroupoids
2.5 Recognizing animae
AnimaTargets
SCT.VolumeI.Chapter02.Section05.AnimaTargets
ArrowCoproducts
SCT.VolumeI.Chapter02.Section05.ArrowCoproducts
PullbackAnimae
SCT.VolumeI.Chapter02.Section05.PullbackAnimae
Recognition
SCT.VolumeI.Chapter02.Section05.Recognition
2.6 Exercises
HomFamilies
SCT.VolumeI.Chapter02.Section06.HomFamilies
HomIsomorphisms
SCT.VolumeI.Chapter02.Section06.HomIsomorphisms
All named declarations in checked SCT modules
SCT.Calculus.Composition.CompositionSCT.Calculus.Composition.Composition.ObjSCT.Calculus.Composition.Composition.HomSCT.Calculus.Composition.Composition._≈_SCT.Calculus.Composition.Composition.idSCT.Calculus.Composition.Composition._∘_SCT.Calculus.Composition.Composition.reflSCT.Calculus.Composition.Composition.symSCT.Calculus.Composition.Composition.transSCT.Calculus.Composition.Composition.congrSCT.Calculus.Composition.LawsSCT.Calculus.Composition.Laws.assocSCT.Calculus.Composition.Laws.unitˡSCT.Calculus.Composition.Laws.unitʳSCT.Calculus.Composition.CalculationSCT.Calculus.Composition.Calculation.cancel-leftSCT.Calculus.Composition.Calculation.cancel-rightSCT.Calculus.Composition.Calculation.reassociate-fourSCT.Calculus.Pasting.projected-trianglesSCT.Calculus.Squares.comparison-route-pastingSCT.Calculus.Squares.factored-squareSCT.Calculus.Squares.common-frame-pastingSCT.Calculus.Squares.normalized-substitution-squareSCT.Calculus.Squares.normalized-input-squareSCT.Calculus.Squares.change-restriction-squareSCT.Calculus.Squares.compose-input-squareSCT.Calculus.Squares.square-with-tailSCT.Calculus.Squares.composite-square-with-tailSCT.Calculus.Squares.normalize-comparison-routeSCT.Calculus.Squares.NestedRouteSCT.Calculus.Squares.NestedRoute.finishSCT.Calculus.Squares.NestedRoute.beginSCT.Calculus.Squares.NestedRoute.resultSCT.Calculus.Squares.normalization-naturalitySCT.Calculus.Squares.normalized-frame-squareSCT.VolumeI.Chapter01.Section01.Terminal.terminateSCT.VolumeI.Chapter01.Section01.Terminal.terminal-identifications-isEquivSCT.VolumeI.Chapter01.Section01.Terminal.terminal-identificationSCT.VolumeI.Chapter01.Section01.Terminal.IsContractibleSCT.VolumeI.Chapter01.Section01.Terminal.constSCT.VolumeI.Chapter01.Section01.Terminal.ContractionSCT.VolumeI.Chapter01.Section01.Terminal.centerSCT.VolumeI.Chapter01.Section01.Terminal.contractionSCT.VolumeI.Chapter01.Section01.Terminal.contractible-to-contractionSCT.VolumeI.Chapter01.Section01.Terminal.contraction-to-contractibleSCT.VolumeI.Chapter01.Section01.Terminal.terminal-identifications-contractibleSCT.VolumeI.Chapter01.Section01.Terms.EqualSCT.VolumeI.Chapter01.Section01.Terms.TermSCT.VolumeI.Chapter01.Section01.Terms.applySCT.VolumeI.Chapter01.Section01.Terms.pairSCT.VolumeI.Chapter01.Section01.Terms._＝_SCT.VolumeI.Chapter01.Section01.Vocabulary.cSCT.VolumeI.Chapter01.Section01.Vocabulary.mSCT.VolumeI.Chapter01.Section01.Vocabulary.aSCT.VolumeI.Chapter01.Section01.Vocabulary.κSCT.VolumeI.Chapter01.Section01.Vocabulary.ContextSCT.VolumeI.Chapter01.Section01.Vocabulary.absoluteSCT.VolumeI.Chapter01.Section01.Vocabulary.CATSCT.VolumeI.Chapter01.Section01.Vocabulary.isAnSCT.VolumeI.Chapter01.Section01.Vocabulary.MAPSCT.VolumeI.Chapter01.Section01.Vocabulary.idSCT.VolumeI.Chapter01.Section01.Vocabulary._∘_SCT.VolumeI.Chapter01.Section01.Vocabulary.OneSCT.VolumeI.Chapter01.Section01.Vocabulary.one-isAnSCT.VolumeI.Chapter01.Section01.Vocabulary._＝_SCT.VolumeI.Chapter01.Section01.Vocabulary.＝-isAnSCT.VolumeI.Chapter01.Section01.Vocabulary.postWhiskerSCT.VolumeI.Chapter01.Section01.Vocabulary.preWhiskerSCT.VolumeI.Chapter01.Section01.Vocabulary.ANSCT.VolumeI.Chapter01.Section01.Vocabulary.categorySCT.VolumeI.Chapter01.Section01.Vocabulary.witnessSCT.VolumeI.Chapter01.Section01.Vocabulary.extendSCT.VolumeI.Chapter01.Section01.Vocabulary.Obj-absSCT.VolumeI.Chapter01.Section01.Vocabulary._=₁_SCT.VolumeI.Chapter01.Section01.Vocabulary._=₂_SCT.VolumeI.Chapter01.Section01.Vocabulary._=₃_SCT.VolumeI.Chapter01.Section01.Vocabulary.IsEquivSCT.VolumeI.Chapter01.Section01.Vocabulary.inverseSCT.VolumeI.Chapter01.Section01.Vocabulary.left-inverse-lawSCT.VolumeI.Chapter01.Section01.Vocabulary.right-inverse-lawSCT.VolumeI.Chapter01.Section01.Vocabulary.EquivSCT.VolumeI.Chapter01.Section01.Vocabulary.functorSCT.VolumeI.Chapter01.Section01.Vocabulary.isEquivSCT.VolumeI.Chapter01.Section01.Vocabulary._◁_SCT.VolumeI.Chapter01.Section01.Vocabulary._▷_SCT.VolumeI.Chapter01.Section01.Vocabulary._×_SCT.VolumeI.Chapter01.Section01.Vocabulary.pr₁SCT.VolumeI.Chapter01.Section01.Vocabulary.pr₂SCT.VolumeI.Chapter01.Section01.Vocabulary.pairSCT.VolumeI.Chapter01.Section01.Vocabulary.pair-β₁SCT.VolumeI.Chapter01.Section01.Vocabulary.pair-β₂SCT.VolumeI.Chapter01.Section01.Vocabulary.product-isAnSCT.VolumeI.Chapter01.Section02.Coherence.id₌SCT.VolumeI.Chapter01.Section02.Coherence.inv₌SCT.VolumeI.Chapter01.Section02.Coherence.comp₌SCT.VolumeI.Chapter01.Section02.Coherence._⁻¹SCT.VolumeI.Chapter01.Section02.Coherence._∙_SCT.VolumeI.Chapter01.Section02.Coherence._⋆_SCT.VolumeI.Chapter01.Section02.Coherence.hcompSCT.VolumeI.Chapter01.Section02.Coherence.comp-unitˡSCT.VolumeI.Chapter01.Section02.Coherence.comp-unitʳSCT.VolumeI.Chapter01.Section02.Coherence.comp-assocSCT.VolumeI.Chapter01.Section02.Coherence.comp₌-unitˡSCT.VolumeI.Chapter01.Section02.Coherence.comp₌-unitʳSCT.VolumeI.Chapter01.Section02.Coherence.comp₌-assocSCT.VolumeI.Chapter01.Section02.Coherence.comp₌-inverseˡSCT.VolumeI.Chapter01.Section02.Coherence.comp₌-inverseʳSCT.VolumeI.Chapter01.Section02.Coherence.postWhisker-id₌SCT.VolumeI.Chapter01.Section02.Coherence.preWhisker-id₌SCT.VolumeI.Chapter01.Section02.Coherence.postWhisker-comp₌SCT.VolumeI.Chapter01.Section02.Coherence.preWhisker-comp₌SCT.VolumeI.Chapter01.Section02.Coherence.interchangeSCT.VolumeI.Chapter01.Section02.Coherence.SquareCell₌SCT.VolumeI.Chapter01.Section02.Coherence.SquareBoundarySCT.VolumeI.Chapter01.Section02.Coherence.square-boundarySCT.VolumeI.Chapter01.Section02.Coherence.topSCT.VolumeI.Chapter01.Section02.Coherence.bottomSCT.VolumeI.Chapter01.Section02.Coherence.leftSCT.VolumeI.Chapter01.Section02.Coherence.rightSCT.VolumeI.Chapter01.Section02.Coherence.SquareCommutesSCT.VolumeI.Chapter01.Section02.Coherence.associator-naturality-squareSCT.VolumeI.Chapter01.Section02.Coherence.unitˡ-naturality-squareSCT.VolumeI.Chapter01.Section02.Coherence.unitʳ-naturality-squareSCT.VolumeI.Chapter01.Section02.Coherence.TriangleDiagramSCT.VolumeI.Chapter01.Section02.Coherence.triangle-diagramSCT.VolumeI.Chapter01.Section02.Coherence.directSCT.VolumeI.Chapter01.Section02.Coherence.firstSCT.VolumeI.Chapter01.Section02.Coherence.secondSCT.VolumeI.Chapter01.Section02.Coherence.TriangleSourceSCT.VolumeI.Chapter01.Section02.Coherence.TriangleTargetSCT.VolumeI.Chapter01.Section02.Coherence.TriangleCommutesSCT.VolumeI.Chapter01.Section02.Coherence.PentagonDiagramSCT.VolumeI.Chapter01.Section02.Coherence.pentagon-diagramSCT.VolumeI.Chapter01.Section02.Coherence.source-firstSCT.VolumeI.Chapter01.Section02.Coherence.source-secondSCT.VolumeI.Chapter01.Section02.Coherence.target-firstSCT.VolumeI.Chapter01.Section02.Coherence.target-secondSCT.VolumeI.Chapter01.Section02.Coherence.target-thirdSCT.VolumeI.Chapter01.Section02.Coherence.PentagonSourceSCT.VolumeI.Chapter01.Section02.Coherence.PentagonTargetSCT.VolumeI.Chapter01.Section02.Coherence.PentagonCommutesSCT.VolumeI.Chapter01.Section02.Coherence.unitˡ-naturalSCT.VolumeI.Chapter01.Section02.Coherence.unitʳ-naturalSCT.VolumeI.Chapter01.Section02.Coherence.assoc-naturalSCT.VolumeI.Chapter01.Section02.Coherence.associativityPentagonSCT.VolumeI.Chapter01.Section02.Coherence.unitTriangleSCT.VolumeI.Chapter01.Section02.Coherence.comp-pentagonSCT.VolumeI.Chapter01.Section02.Coherence.comp-triangleSCT.VolumeI.Chapter01.Section02.HorizontalComposition.hcomp-comp₌SCT.VolumeI.Chapter01.Section02.IdentificationSquares.identity-square₌SCT.VolumeI.Chapter01.Section02.IdentificationSquares.paste-square₌SCT.VolumeI.Chapter01.Section02.IdentificationSquares.adjoin-square₌SCT.VolumeI.Chapter01.Section02.IdentificationSquares.transpose-square₌SCT.VolumeI.Chapter01.Section02.IdentificationSquares.inverse-square₌SCT.VolumeI.Chapter01.Section02.IdentificationSquares.inv-comp-square₌SCT.VolumeI.Chapter01.Section02.IdentificationSquares.post-square₌SCT.VolumeI.Chapter01.Section02.IdentificationSquares.pre-square₌SCT.VolumeI.Chapter01.Section02.IdentificationSquares.hcomp-square₌-outerSCT.VolumeI.Chapter01.Section02.IdentificationSquares.hcomp-square₌-innerSCT.VolumeI.Chapter01.Section02.IdentificationSquares.replace-sides₌SCT.VolumeI.Chapter01.Section02.IdentificationSquares.replace-edges₌SCT.VolumeI.Chapter01.Section02.IdentificationSquares.constant-square₌SCT.VolumeI.Chapter01.Section02.IdentificationSquares.unconst-sides₌SCT.VolumeI.Chapter01.Section02.IdentificationSquares.const-sides₌SCT.VolumeI.Chapter01.Section02.IdentificationSquares.project-compositeSCT.VolumeI.Chapter01.Section02.IdentificationSquares.postwhiskered-compositeSCT.VolumeI.Chapter01.Section02.IdentificationSquares.prewhiskered-compositeSCT.VolumeI.Chapter01.Section02.IdentificationSquares.fill-cube₌SCT.VolumeI.Chapter01.Section02.Naturality.Inputs₂SCT.VolumeI.Chapter01.Section02.Naturality.inputs₂SCT.VolumeI.Chapter01.Section02.Naturality.firstSCT.VolumeI.Chapter01.Section02.Naturality.secondSCT.VolumeI.Chapter01.Section02.Naturality.Inputs₃SCT.VolumeI.Chapter01.Section02.Naturality.inputs₃SCT.VolumeI.Chapter01.Section02.Naturality.firstSCT.VolumeI.Chapter01.Section02.Naturality.secondSCT.VolumeI.Chapter01.Section02.Naturality.thirdSCT.VolumeI.Chapter01.Section02.Naturality.OperationSCT.VolumeI.Chapter01.Section02.Naturality.valueSCT.VolumeI.Chapter01.Section02.Naturality.actionSCT.VolumeI.Chapter01.Section02.Naturality.NaturalityAtSCT.VolumeI.Chapter01.Section02.Naturality.NaturalitySCT.VolumeI.Chapter01.Section02.Naturality.NaturalIdentificationSCT.VolumeI.Chapter01.Section02.Naturality.componentSCT.VolumeI.Chapter01.Section02.Naturality.naturalitySCT.VolumeI.Chapter01.Section02.Naturality.HomChangeSCT.VolumeI.Chapter01.Section02.Naturality.PairChangeSCT.VolumeI.Chapter01.Section02.Naturality.TripleChangeSCT.VolumeI.Chapter01.Section02.Naturality.InputSCT.VolumeI.Chapter01.Section02.Naturality.PostSCT.VolumeI.Chapter01.Section02.Naturality.PreSCT.VolumeI.Chapter01.Section02.Naturality.ComposeSCT.VolumeI.Chapter01.Section02.Naturality.SubstituteSCT.VolumeI.Chapter01.Section02.Naturalit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nv-leftSCT.VolumeI.Chapter01.Section02.Specialization.comp-inv-rightSCT.VolumeI.Chapter01.Section02.Specialization.inv-comp-rightSCT.VolumeI.Chapter01.Section02.Specialization.reassociateFourSCT.VolumeI.Chapter01.Section02.Specialization.unitˡ-naturalSCT.VolumeI.Chapter01.Section02.Specialization.unitʳ-naturalSCT.VolumeI.Chapter01.Section02.Specialization.assoc-naturalSCT.VolumeI.Chapter01.Section02.Specialization.hcomp-id-outerSCT.VolumeI.Chapter01.Section02.Specialization.hcomp-id-innerSCT.VolumeI.Chapter01.Section02.Specialization.hcomp-id₌SCT.VolumeI.Chapter01.Section02.Specialization.postWhisker-comp₌SCT.VolumeI.Chapter01.Section02.Specialization.preWhisker-comp₌SCT.VolumeI.Chapter01.Section02.Specialization.interchangeSCT.VolumeI.Chapter01.Section02.Specialization.interchange-fixedOuterSCT.VolumeI.Chapter01.Section02.Specialization.interchange-fixedInnerSCT.VolumeI.Chapter01.Section02.Whiskering.postWhisker-idSCT.VolumeI.Chapter01.Section02.Whiskering.preWhisker-idSCT.VolumeI.Chapter01.Section02.Whiskering.postWhisker-compSCT.VolumeI.Chapter01.Section02.Whiskering.preWhisker-compSCT.VolumeI.Chapter01.Section02.Whiskering.whisker-mixedSCT.VolumeI.Chapter01.Section02.Whiskering.postWhisker-comp-naturalitySCT.VolumeI.Chapter01.Section03.Equivalences.ReflectsIdentificationsSCT.VolumeI.Chapter01.Section03.Equivalences.equiv-reflectSCT.VolumeI.Chapter01.Section03.Equivalences.SectionSCT.VolumeI.Chapter01.Section03.Equivalences.sectionSCT.VolumeI.Chapter01.Section03.Equivalences.section-lawSCT.VolumeI.Chapter01.Section03.Equivalences.RetractionSCT.VolumeI.Chapter01.Section03.Equivalences.retractionSCT.VolumeI.Chapter01.Section03.Equivalences.retraction-lawSCT.VolumeI.Chapter01.Section03.Equivalences.equiv-sectionSCT.VolumeI.Chapter01.Section03.Equivalences.equiv-retractionSCT.VolumeI.Chapter01.Section03.Equivalences.section-retraction-equalSCT.VolumeI.Chapter01.Section03.Equivalences.section-retraction-isEquivSCT.VolumeI.Chapter01.Section03.Equivalences.inverse-uniqueSCT.VolumeI.Chapter01.Section03.Equivalences.id-isEquivSCT.VolumeI.Chapter01.Section03.Equivalences.equiv-inverseSCT.VolumeI.Chapter01.Section03.Equivalences.equiv-transportSCT.VolumeI.Chapter01.Section03.Equivalences.equiv-composeSCT.VolumeI.Chapter01.Section03.Equivalences.equiv-cancel-rightSCT.VolumeI.Chapter01.Section03.Equivalences.equiv-cancel-leftSCT.VolumeI.Chapter01.Section03.Equivalences.square-source-map-isEquivSCT.VolumeI.Chapter01.Section03.Equivalences.square-functor-isEquivSCT.VolumeI.Chapter01.Section03.Equivalences.TwoOutOfSixSCT.VolumeI.Chapter01.Section03.Equivalences.firstSCT.VolumeI.Chapter01.Section03.Equivalences.middleSCT.VolumeI.Chapter01.Section03.Equivalences.lastSCT.VolumeI.Chapter01.Section03.Equivalences.compositeSCT.VolumeI.Chapter01.Section03.Equivalences.two-out-of-sixSCT.VolumeI.Chapter01.Section03.Equivalences.terminal-unique₂SCT.VolumeI.Chapter01.Section03.Equivalences.contractible-sourceSCT.VolumeI.Chapter01.Section03.Equivalences.contractible-uniqueSCT.VolumeI.Chapter01.Section03.Factorizations.FactorizationSCT.VolumeI.Chapter01.Section03.Factorizations.factorSCT.VolumeI.Chapter01.Section03.Factorizations.triangleSCT.VolumeI.Chapter01.Section03.Factorizations.factorization-retargetSCT.VolumeI.Chapter01.Section03.Factorizations.factorization-restrictSCT.VolumeI.Chapter01.Section03.Factorizations.square-factorizationSCT.VolumeI.Chapter01.Section03.Factorizations.factorization-along-squareSCT.VolumeI.Chapter01.Section03.Factorizations.factor-through-equivSCT.VolumeI.Chapter01.Section03.Factorizations.factorization-from-equivalent-sourceSCT.VolumeI.Chapter01.Section03.Factorizations.factor-and-reflection-isEquivSCT.VolumeI.Chapter01.Section03.Factorizations.chosenSCT.VolumeI.Chapter01.Section03.Factorizations.gSCT.VolumeI.Chapter01.Section03.Factorizations.βSCT.VolumeI.Chapter01.Section03.Factorizations.imageSCT.VolumeI.Chapter01.Section03.Factorizations.ExtensionSCT.VolumeI.Chapter01.Section03.Factorizations.extensionSCT.VolumeI.Chapter01.Section03.Factorizations.extension-triangleSCT.VolumeI.Chapter01.Section03.Factorizations.extension-retargetSCT.VolumeI.Chapter01.Section03.Identifications.EndpointTransport.changeEndpointsSCT.VolumeI.Chapter01.Section03.Identifications.EndpointTransport.changeEndpoints-congSCT.VolumeI.Chapter01.Section03.Identifications.EndpointTransport.changeEndpoints-compSCT.VolumeI.Chapter01.Section03.Identifications.EndpointTransport.changeEndpoints-idSCT.VolumeI.Chapter01.Section03.Identifications.EndpointTransport.changeEndpoints-comp₃SCT.VolumeI.Chapter01.Section03.Identifications.EndpointTransport.changeEndpoints-iteratedSCT.VolumeI.Chapter01.Section03.Identifications.EndpointTransport.changeEndpoints-reflectSCT.VolumeI.Chapter01.Section03.Identifications.EndpointTransport.square-to-changeEndpointsSCT.VolumeI.Chapter01.Section03.Identifications.EndpointTransport.changeEndpoints-to-squareSCT.VolumeI.Chapter01.Section03.Identifications.EndpointTransport.postWhisker-changeEndpointsSCT.V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