數(shù)學(xué)工作者必知的范疇學(xué) 第2版

內(nèi)容概要

This second edition of "Categories Work" adds two new chapters on topics of active interest. One is on symmetric monoidal categories and braided monoidal categories and the coherence theorems for them--items of interest in their own right and also in view of their use in string theory in quantum field theory. The second new chapter describes 2-categories and the higher-dimensional categories that have recently come into prominence. In addition, the bibliography has been expanded to cover some of the many other recent advances concerning categories.

書籍目錄

PrefacetotheSecondEditionPrefacetotheFirstEditionIntroductionⅠ.Categories，F(xiàn)unctors，andNaturalTransformations  1.AxiomsforCategories  2.Categories  3.Functors  4.NaturalTransformations  5.Monics，Epis，andZeros  6.Foundations  7.LargeCategories  8.Hom-SetsⅡ.ConstructionsonCategories  1.Duality  2.ContravarianceandOpposites  3.ProductsofCategories  4.FunctorCategories  5.TheCategoryofAllCategories  6.CommaCategories  7.GraphsandFreeCategories  8.QuotientCategoriesⅢ.UniversalsandLimits  1.UniversalArrows  2.TheYonedaLemma  3.CoproductsandColimits  4.ProductsandLimits  5.CategorieswithFiniteProducts  6.GroupsinCategories  7.ColimitsofRepresentableFunctorsⅣ.Adjoints  1.Adjunctions  2.ExamplesofAdjoints  3.ReflectiveSubcategories  4.EquivalenceofCategories  5.AdjointsforPreorders  6.CartesianClosedCategories  7.TransformationsofAdjoints  8.CompositionofAdjoints  9.SubsetsandCharacteristicFunctions  10.CategoriesLikeSetsⅤ.Limits  1.CreationofLimits  2.LimitsbyProductsandEqualizers  3.LimitswithParameters  4.PreservationofLimits  5.AdjointsonLimits  6.Freyd'sAdjointFunctorTheorem  7.SubobjectsandGenerators  8.TheSpecialAdjointFunctorTheorem  9.AdjointsinTopologyⅥ.MonadsandAlgebras  1.MonadsinaCategory  2.AlgebrasforaMonad  3.TheComparisonwithAlgebras  4.WordsandFreeSemigroups  5.FreeAlgebrasforaMonad  6.SplitCoequalizers  7.Beck'sTheorem  8.AlgebrasAreT-Algebras  9.CompactHausdorffSpacesⅦ.Monoids  1.MonoidalCategories  2.Coherence  3.Monoids  4.Actions  5.TheSimplicialCategory  6.MonadsandHomology  7.ClosedCategories  8.CompactlyGeneratedSpaces  9.LoopsandSuspensionsⅧ.AbelianCategories  1.KernelsandCokernels  2.AdditiveCategories  3.AbelianCategories  4.DiagramLemmasⅨ.SpecialLimits  1.FilteredLimits  2.InterchangeofLimits  3.FinalFunctors  4.DiagonalNaturality  5.Ends  6.Coends  7.EndswithParameters  8.IteratedEndsandLimitsⅩ.KanExtensions  1.AdjointsandLimits  2.WeakUniversality  3.TheKanExtension  4.KanExtensionsasCoends  5.PointwiseKanExtensions  6.Density  7.AllConceptsAreKanExtensionsⅪ.SymmetryandBraidinginMonoidalCategories  1.SymmetricMonoidalCategories  2.MonoidalFunctors  3.StrictMonoidalCategories  4.TheBraidGroupsBnandtheBraidCategory  5.BraidedCoherence  6.PerspectivesⅫ.StructuresinCategories  1.InternalCategories  2.TheNerveofaCategory  3.2-Categories  4.Operationsin2-Categories  5.Single-SetCategories  6.Bicategories  7.ExamplesofBicategories  8.CrossedModulesandCategoriesinGrpAppendix.FoundationsTableofStandardCategories:ObjectsandArrowsTableofTerminologyBibliographyIndex

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