《Categories for the Working Mathematician》是2003年世界圖書出版公司出版的圖書。
基本介紹
- 中文名：Categories for the Working Mathematician
- 作者：Saunders Mac Lane
- 出版社：世界圖書出版公司出版社
- 出版時間：2003年
- 開本：128 開
- 裝幀：平裝-膠訂
- ISBN：9787506260084
內容簡介,圖書目錄,
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.
圖書目錄
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
