{ "agda": "Agda version 2.8.0-3d04bac", "aggregate": "SCT.WebEdition", "verification_mode": "checked current snapshot", "manuscript_revision": "81a6a2136eb6fecddcd5e762be865552437329f1", "frontmatter": [ { "slug": "introduction", "title": "Introduction" }, { "slug": "overview-of-the-axioms", "title": "Overview of the axioms" } ], "sections": [ { "title": "The basic vocabulary", "label": "sec:External_Theory" }, { "title": "Coherences", "label": "sec:Coherences" }, { "title": "Equivalences of categories", "label": "sec:Equivalence_Of_Categories" }, { "title": "Mapping animae", "label": "sec:Mapping_Animae" }, { "title": "Initial categories and coproducts", "label": "sec:Initial_Categories_And_Coproducts" }, { "title": "Pullbacks of categories", "label": "sec:Pullbacks_Of_Categories" }, { "title": "Functor categories", "label": "sec:Functor_Categories" }, { "title": "Pushout squares", "label": "sec:Pushouts_Of_Categories" }, { "title": "Morphisms and diagrams", "label": "sec:Morphisms_and_Diagrams" }, { "title": "The Segal axiom", "label": "sec:The_Segal_Axiom" }, { "title": "The Rezk axiom", "label": "sec:Rezk_Axiom" }, { "title": "Groupoids", "label": "sec:Groupoids" }, { "title": "Recognizing animae", "label": "sec:Recognizing_Animae" }, { "title": "Exercises", "label": "web:chapter02-exercises" }, { "title": "Subcategories", "label": "sec:Subcategories" }, { "title": "Full subcategories", "label": "sec:Full_Subcategories" }, { "title": "Localizations", "label": "sec:Localizations_Of_Categories" }, { "title": "Geometric realizations", "label": "sec:Geometric_Realizations" }, { "title": "Exponentiable functors", "label": "sec:Exponentiable_Functors" }, { "title": "Joins", "label": "sec:Joins" }, { "title": "Slice categories", "label": "sec:Slice_Categories_From_Joins" }, { "title": "Exercises \\texorpdfstring{\\Cref{chap:Basic_Synthetic_Category_Theory}}{Chapter 3}", "label": "web:chapter03-exercises" } ], "declaration_mappings": 1186, 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"SCT.VolumeI.Chapter01.Section05.Initial", "SCT.VolumeI.Chapter01.Section06.ConeFramings", "SCT.VolumeI.Chapter01.Section06.ConeIdentifications", "SCT.VolumeI.Chapter01.Section06.ConePasting", "SCT.VolumeI.Chapter01.Section06.ConeTransport", "SCT.VolumeI.Chapter01.Section06.ConeUniversality", "SCT.VolumeI.Chapter01.Section06.Cones", "SCT.VolumeI.Chapter01.Section06.CoproductCover", "SCT.VolumeI.Chapter01.Section06.CoproductDescent", "SCT.VolumeI.Chapter01.Section06.DiagonalPullbacks", "SCT.VolumeI.Chapter01.Section06.Distributivity", "SCT.VolumeI.Chapter01.Section06.EmbeddingPullbackSquares", "SCT.VolumeI.Chapter01.Section06.Embeddings", "SCT.VolumeI.Chapter01.Section06.FramedConePasting", "SCT.VolumeI.Chapter01.Section06.FramedConeTransport", "SCT.VolumeI.Chapter01.Section06.MappingPullbacks", "SCT.VolumeI.Chapter01.Section06.NestedPullbacks", "SCT.VolumeI.Chapter01.Section06.PastingLemma", "SCT.VolumeI.Chapter01.Section06.ProductPullbacks", "SCT.VolumeI.Chapter01.Section06.ProjectionFibers", "SCT.VolumeI.Chapter01.Section06.PullbackArrowChange", "SCT.VolumeI.Chapter01.Section06.PullbackConstructions", "SCT.VolumeI.Chapter01.Section06.PullbackFunctoriality", "SCT.VolumeI.Chapter01.Section06.PullbackSquares", "SCT.VolumeI.Chapter01.Section06.Pullbacks", "SCT.VolumeI.Chapter01.Section06.Representability", "SCT.VolumeI.Chapter01.Section06.RepresentabilityDiagonal", "SCT.VolumeI.Chapter01.Section06.SuccessiveCospans", "SCT.VolumeI.Chapter01.Section06.UniversalConeIdentifications", "SCT.VolumeI.Chapter01.Section06.UniversalCoproducts", "SCT.VolumeI.Chapter01.Section07.CoreOfFun", "SCT.VolumeI.Chapter01.Section07.Currying", "SCT.VolumeI.Chapter01.Section07.DiagramRepresentations", "SCT.VolumeI.Chapter01.Section07.Evaluation", "SCT.VolumeI.Chapter01.Section07.EvaluationRepresentation", "SCT.VolumeI.Chapter01.Section07.EvaluationSubstitution", "SCT.VolumeI.Chapter01.Section07.ExponentialLaw", "SCT.VolumeI.Chapter01.Section07.FunctorCategories", "SCT.VolumeI.Chapter01.Section07.FunctorConeRestriction", "SCT.VolumeI.Chapter01.Section07.FunctorCones", "SCT.VolumeI.Chapter01.Section07.FunctorProducts", "SCT.VolumeI.Chapter01.Section07.FunctorProperties", "SCT.VolumeI.Chapter01.Section07.FunctorPullbacks", "SCT.VolumeI.Chapter01.Section07.Functoriality", "SCT.VolumeI.Chapter01.Section07.PostEvaluationSubstitution", "SCT.VolumeI.Chapter01.Section07.PreEvaluationSubstitution", "SCT.VolumeI.Chapter01.Section08.CoconeCommonAxis", "SCT.VolumeI.Chapter01.Section08.Cocones", "SCT.VolumeI.Chapter01.Section08.FunctorMappingOutEvaluation", "SCT.VolumeI.Chapter01.Section08.FunctorPushoutCriterion", "SCT.VolumeI.Chapter01.Section08.MappingOutEvaluation", "SCT.VolumeI.Chapter01.Section08.PushoutSquares", "SCT.VolumeI.Chapter01.Section09.NamedEvaluation", "SCT.VolumeI.Chapter01.Section09.RelativeInverseLaws", "SCT.VolumeI.Chapter02.Section01.CoreCoproducts", "SCT.VolumeI.Chapter02.Section01.CoreInclusions", "SCT.VolumeI.Chapter02.Section01.HomAndSlices", "SCT.VolumeI.Chapter02.Section01.IdentityFamilyPostcomposition", "SCT.VolumeI.Chapter02.Section01.IdentityFamilyRestriction", "SCT.VolumeI.Chapter02.Section01.IdentityFamilyTransport", "SCT.VolumeI.Chapter02.Section01.InsertionSectionComparison", "SCT.VolumeI.Chapter02.Section01.InsertionSectionEvaluation", "SCT.VolumeI.Chapter02.Section01.MorphismFamilyComparisons", "SCT.VolumeI.Chapter02.Section01.MorphismFamilyOperations", "SCT.VolumeI.Chapter02.Section01.MorphismFamilyPostcomposition", "SCT.VolumeI.Chapter02.Section01.MorphismFamilyPostcompositionPasting", "SCT.VolumeI.Chapter02.Section01.MorphismFamilyReflection", "SCT.VolumeI.Chapter02.Section01.MorphismFraming", "SCT.VolumeI.Chapter02.Section01.MorphismFunctor", "SCT.VolumeI.Chapter02.Section01.Morphisms", "SCT.VolumeI.Chapter02.Section01.PointEvaluationAction", "SCT.VolumeI.Chapter02.Section01.PointEvaluationComposition", "SCT.VolumeI.Chapter02.Section01.PointEvaluationCorners", "SCT.VolumeI.Chapter02.Section01.PointEvaluationIdentity", "SCT.VolumeI.Chapter02.Section01.PointEvaluationParameters", "SCT.VolumeI.Chapter02.Section01.PointEvaluationPostcomposition", "SCT.VolumeI.Chapter02.Section01.PointEvaluationShapes", "SCT.VolumeI.Chapter02.Section01.PostcompositionPointNaturality", "SCT.VolumeI.Chapter02.Section01.PostcompositionRestriction", "SCT.VolumeI.Chapter02.Section01.RepresentedDiagramPostcomposition", "SCT.VolumeI.Chapter02.Section01.RestrictedDiagramEvaluation", "SCT.VolumeI.Chapter02.Section01.SliceFibers", "SCT.VolumeI.Chapter02.Section01.SquareGluing", "SCT.VolumeI.Chapter02.Section01.TriangleCore", "SCT.VolumeI.Chapter02.Section01.Triangles", "SCT.VolumeI.Chapter02.Section01.WalkingMorphism", "SCT.VolumeI.Chapter02.Section01.WalkingTriangle", "SCT.VolumeI.Chapter02.Section02.CommonDiagramDiagonal", "SCT.VolumeI.Chapter02.Section02.ConstantRestrictionEvaluation", "SCT.VolumeI.Chapter02.Section02.FixedInputMorphismFamilies", "SCT.VolumeI.Chapter02.Section02.FramedCornerPostcomposition", "SCT.VolumeI.Chapter02.Section02.FramedDiagramTransport", "SCT.VolumeI.Chapter02.Section02.FramedSquareCommutativity", "SCT.VolumeI.Chapter02.Section02.FramedSquares", "SCT.VolumeI.Chapter02.Section02.FramedTrianglePresentations", "SCT.VolumeI.Chapter02.Section02.GluedFramedSquares", "SCT.VolumeI.Chapter02.Section02.GluedTrianglePresentations", "SCT.VolumeI.Chapter02.Section02.Interchange", "SCT.VolumeI.Chapter02.Section02.InternalComposition", "SCT.VolumeI.Chapter02.Section02.MorphismComposition", "SCT.VolumeI.Chapter02.Section02.MorphismCompositionAssociativity", "SCT.VolumeI.Chapter02.Section02.MorphismCompositionComparisons", "SCT.VolumeI.Chapter02.Section02.MorphismCompositionPostcomposition", "SCT.VolumeI.Chapter02.Section02.MorphismCompositionPresentation", "SCT.VolumeI.Chapter02.Section02.MorphismCompositionTransport", 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