数学工作者必知的范畴学 第2版

图书标准信息

• 作者 M.Lang 编
• 出版社 世界图书出版公司
• 出版时间 2003-06
• 版次 2
• ISBN 9787506260084
• 定价 39.00元
• 装帧 平装
• 开本 其他
• 纸张 胶版纸
• 页数 314页
• 正文语种 英语
• 原版书名 Categories for the Working Mathematician

【内容简介】

Thissecondeditionof"CategoriesWork"addstwonewchaptersontopicsofactiveinterest.Oneisonsymmetricmonoidalcategoriesandbraidedmonoidalcategoriesandthecoherencetheoremsforthem——itemsofinterestintheirownrightandalsoinviewoftheiruseinstringtheoryinquantumfieldtheory.Thesecondnewchapterdescribes2-categoriesandthehigher-dimensionalcategoriesthathaverecentlycomeintoprominence.Inaddition,thebibliographyhasbeenexpandedtocoversomeofthemanyotherrecentadvancesconcerningcategories.

【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