数学工作者必知的范畴学(第2版)(英文版)

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. 这是M.Lang编著的这本《《数学工作者必知的范 畴学（第2版）（英文版）》》的英文简介。

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，andZeros 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