數學工作者必知的範疇學

《數學工作者必知的範疇學(第2版)》內容簡介：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.

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