| PrefacetotheSecondEdition PrefacetotheFirstEdition Introduction Ⅰ.Categories，Functors，andNaturalTransformations 1.AxiomsforCategories 2.Categories 3.Functors 4.NaturalTransformations 5.Monics，Epis，andZeros 6.Foundations 7.LargeCategories 8.Hom-Sets Ⅱ.ConstructionsonCategories 1.Duality 2.ContravarianceandOpposites 3.ProductsofCategories 4.FunctorCategories 5.TheCategoryofAllCategories 6.CommaCategories 7.GraphsandFreeCategories 8.QuotientCategories Ⅲ.UniversalsandLimits 1.UniversalArrows 2.TheYonedaLemma 3.CoproductsandColimits 4.ProductsandLimits 5.CategorieswithFiniteProducts 6.GroupsinCategories 7.ColimitsofRepresentableFunctors Ⅳ.Adjoints 1.Adjunctions 2.ExamplesofAdjoints 3.ReflectiveSubcategories 4.EquivalenceofCategories 5.AdjointsforPreorders 6.CartesianClosedCategories 7.TransformationsofAdjoints 8.CompositionofAdjoints 9.SubsetsandCharacteristicFunctions 10.CategoriesLikeSets Ⅴ.Limits 1.CreationofLimits 2.LimitsbyProductsandEqualizers 3.LimitswithParameters 4.PreservationofLimits 5.AdjointsonLimits 6.Freyd'sAdjointFunctorTheorem 7.SubobjectsandGenerators 8.TheSpecialAdjointFunctorTheorem 9.AdjointsinTopology Ⅵ.MonadsandAlgebras 1.MonadsinaCategory 2.AlgebrasforaMonad 3.TheComparisonwithAlgebras 4.WordsandFreeSemigroups 5.FreeAlgebrasforaMonad 6.SplitCoequalizers 7.Beck'sTheorem 8.AlgebrasAreT-Algebras 9.CompactHausdorffSpaces Ⅶ.Monoids 1.MonoidalCategories 2.Coherence 3.Monoids 4.Actions 5.TheSimplicialCategory 6.MonadsandHomology 7.ClosedCategories 8.CompactlyGeneratedSpaces 9.LoopsandSuspensions Ⅷ.AbelianCategories 1.KernelsandCokernels 2.AdditiveCategories 3.AbelianCategories 4.DiagramLemmas Ⅸ.SpecialLimits 1.FilteredLimits 2.InterchangeofLimits 3.FinalFunctors 4.DiagonalNaturality 5.Ends 6.Coends 7.EndswithParameters 8.IteratedEndsandLimits Ⅹ.KanExtensions 1.AdjointsandLimits 2.WeakUniversality 3.TheKanExtension 4.KanExtensionsasCoends 5.PointwiseKanExtensions 6.Density 7.AllConceptsAreKanExtensions Ⅺ.SymmetryandBraidinginMonoidalCategories 1.SymmetricMonoidalCategories 2.MonoidalFunctors 3.StrictMonoidalCategories 4.TheBraidGroupsBnandtheBraidCategory 5.BraidedCoherence 6.Perspectives Ⅻ.StructuresinCategories 1.InternalCategories 2.TheNerveofaCategory 3.2-Categories 4.Operationsin2-Categories 5.Single-SetCategories 6.Bicategories 7.ExamplesofBicategories 8.CrossedModulesandCategoriesinGrp Appendix.Foundations TableofStandardCategories:ObjectsandArrows TableofTerminology Bibliography Index |
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