数学工作者必知的范畴学（第二版）

定　价：¥39.00

作　者：	M.Lang
出版社：	世界图书出版公司
丛编项：
标　签：	数学理论

ISBN：	9787503669279	出版时间：	2003-06-01	包装：	平装
开本：	24	页数：	314	字数：

内容简介

　　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.本书为英文版。

作者简介

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图书目录

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