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数学工作者必知的范畴学 第2版2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

数学工作者必知的范畴学 第2版
  • M.Lang 著
  • 出版社： 北京：世界图书出版公司北京公司
  • ISBN：7506260085
  • 出版时间：2003
  • 标注页数：314页
  • 文件大小：45MB
  • 文件页数：327页
  • 主题词：工具书

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图书目录

Introduction1

Ⅰ．Categories,Functors,and Natural Transformations7

1．Axioms for Categories7

2．Categories10

3．Functors13

4．Natural Transformations16

5．Monics,Epis,and Zeros19

6．Foundations21

7．Large Categories24

8．Hom-Sets27

Ⅱ．Constructions on Categories31

1．Duality31

2．Contravariance and Opposites33

3．Products of Categories36

4．Functor Categories40

5．The Category of All Categories42

6．Comma Categories45

7．Graphs and Free Categories48

8．Quotient Categories51

Ⅲ．Universals and Limits55

1．Universal Arrows55

2．The Yoneda Lemma59

3．Coproducts and Colimits62

4．Products and Limits68

5．Categories with Finite Products72

6．Groups in Categories75

7．Colimits of Representable Functors76

Ⅳ．Adjoints79

1．Adjunctions79

2．Examples of Adjoints86

3．Reffective Subcategories90

4．Equivalence of Categories92

5．Adjoints for Preorders95

6．Cartesian Closed Categories97

7．Transformations of Adjoints99

8．Composition of Adjoints103

9．Subsets and Characteristic Functions105

10．Categories Like Sets106

Ⅴ．Limits109

1．Creation of Limits109

2．Limits by Products and Equalizers112

3．Limits with Parameters115

4．Preservation of Limits116

5．Adjoints on Limits118

6．Freyd's Adjoint Functor Theorem120

7．Subobjects and Generators126

8．The Special Adjoint Functor Theorem128

9．Adjoints in Topology132

Ⅵ．Monads and Algebras137

1．Monads in a Category137

2．Algebras for a Monad139

3．The Comparison with Algebras142

4．Words and Free Semigroups144

5．Free Algebras for a Monad147

6．Split Coequalizers149

7．Beck's Theorem151

8．Algebras Are T-Algebras156

9．Compact Hausdorff Spaces157

Ⅶ．Monoids161

1．Monoidal Categories161

2．Coherence165

3．Monoids170

4．Actions174

5．The Simplicial Category175

6．Monads and Homology180

7．Closed Categories184

8．Compactly Generated Spaces185

9．Loops and Suspensions188

Ⅷ．Abelian Categories191

1．Kernels and Cokernels191

2．Additive Categories194

3．Abelian Categories198

4．Diagram Lemmas202

Ⅸ．Special Limits211

1．Filtered Limits211

2．Interchange of Limits214

3．Final Functors217

4．Diagonal Naturality218

5．Ends222

6．Coends226

7．Ends with Parameters228

8．Iterated Ends and Limits230

Ⅹ．Kan Extensions233

1．Adjoints and Limits233

2．Weak Universality235

3．The Kan Extension236

4．Kan Extensions as Coends240

5．Pointwise Kan Extensions243

6．Density245

7．All Concepts Are Kan Extensions248

Ⅺ．Symmetry and Braiding in Monoidal Categories251

1．Symmetric Monoidal Categories251

2．Monoidal Functors255

3．Strict Monoidal Categories257

4．The Braid Groups Bn and the Braid Category260

5．Braided Coherence263

6．Perspectives266

Ⅻ．Structures in Categories267

1．Internal Categories267

2．The Nerve of a Category270

3．2-Categories272

4．Operations in 2-Categories276

5．Single-Set Categories279

6．Bicategories281

7．Examples of Bicategories283

8．Crossed Modules and Categories in Grp285

Appendix．Foundations289

Table of Standard Categories：Objects and Arrows293

Table of Terminology295

Bibliography297

Index303

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