数学工作者必知的范畴学(第2版)(英文版)
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作者Saunders Mac Lane|责编:刘慧//高蓉
出版社世界图书出版公司
ISBN9787506260084
出版时间2003-09
装帧其他
开本其他
定价69元
货号30934967
上书时间2024-06-27
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目录
Preface to the Second Edition
Preface to the First Edition
Introduction
Ⅰ.Categories, Functors, and Natural Transformations
1.Axioms for Categories
2.Categories
3.Functors
4.Natural Transformations
5.Monics, Epis, and Zeros
6.Foundations
7.Large Categories
8.Hom-Sets
Ⅱ.Constructionson Categories
1.Duality
2.Contravarianceand Opposites
3.Products of Categories
4.Functor Categories
5.TheCategory of All Categories
6.Comma Categories
7.Graphs and FreeCategories
8.Quotient Categories
Ⅲ.Universals and Limits
1.Universal Arrows
2.The Yoneda Lemma
3.Coproducts and Colimits
4.Products and Limits
5.Categories with Finite Products
6.Groups in Categories
7.Colimits of Representable Functors
Ⅳ.Adjoints
1.Adjunctions
2.Examples of Adjoints
3.Reflective Subcategories
4.Equivalence of Categories
5.Adjoints for Preorders
6.Cartesian Closed Categories
7.Transformations of Adjoints
8.Composition of Adjoints
9.Subsets and Characteristic Functions
10.Categories LikeSets
Ⅴ.Limits
1.Creation of Limits
2.Limitsby Productsand Equalizers
3.Limits with Parameters
4.Preservation of Limits
5.Adjointson Limits
6.Freyd's Adjoint Functor Theorem
7.Subobjects and Generators
8.TheSpecial Adjoint Functor Theorem
9.Adjoints in Topology
Ⅵ.Monads and Algebras
1.Monadsina Category
2.Algebras for a Monad
3.The Comparison with Algebras
4.Words and Free Semigroups
5.Free Algebras for a Monad
6.Split Coequalizers
7.Beck's Theorem
8.Algebras Are T-Algebras
9.Compact Hausdorff Spaces
Ⅶ.Monoids
1.Monoidal Categories
2.Coherence
3.Monoids
4.Actions
5.The Simplicial Category
6.Monads and Homology
7.Closed Categories
8.Compactly Generated Spaces
9.Loopsand Suspensions
Ⅷ.Abelian Categories
1.Kernels and Cokernels
2.Additive Categories
3.Abelian Categories
4.Diagram Lemmas
Ⅸ.Special Limits
1.Filtered Limits
2.Interchange of Limits
3.Final Functors
4.Diagonal Naturality
5.Ends
6.Coends
7.Endswith Parameters
8.Iterated Endsand Limits
Ⅹ.Kan Extensions
1.Adjointsand Limits
2.Weak Universality
3.The Kan Extension
4.Kan Extensionsas Coends
5.Pointwise Kan Extensions
6.Density
7.All Concepts Are Kan Extensions
Ⅺ.Symmetry and Braidingin Monoidal Categories
1.Symmetric Monoidal Categories
2.Monoidal Functors
3.Strict Monoidal Categories
4.The Braid Groups Bnand the Braid Category
5.Braided Coherence
6.Perspectives
Ⅻ.Structures in Categories
1.Internal Categories
2.TheNerve of a Category
3.2-Categories
4.Operations in 2-Categories
5.Single-Set Categories
6.Bicategories
7.Examples of Bicategories
8.Crossed Modules and Categories in Grp
Appendix.Foundations
Table of Standard Categories: Objects and Arrows
Table of Terminology
Bibliography
Index
内容摘要
《数学工作者必知的范畴学》第二版的“分类工作”增加了两个新的章节的主题积极兴趣。一个是关于对称幺半群范畴和辫状幺半群范畴以及它们的相干性定理——它们本身就有兴趣，也考虑到它们在量子场论中弦理论中的应用。第二个新的章节描述了2-范畴和最近变得突出的高维范畴。此外，书目已扩大，涵盖了许多其他最新进展的类别。
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