目錄
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
?.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
?.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
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