Abstract and concrete categories: the joy of cats

Jiri Adamek, Horst Herrlich, George E. Strecker9780471609223, 0471609226

This up-to-date introductory treatment employs category theory to explore the theory of structures. Its unique approach stresses concrete categories and presents a systematic view of factorization structures, offering a unifying perspective on earlier work and summarizing recent developments. Numerous examples, ranging from general to specific, illuminate the text. 1990 edition, updated 2004.

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Table of contents :
Preface to the Online Edition……Page 3
Preface……Page 4
0 Introduction……Page 7
Motivation……Page 11
Foundations……Page 13
I Categories, Functors, and Natural Transformations……Page 15
Categories and functors……Page 21
Subcategories……Page 48
Concrete categories and concrete functors……Page 61
Natural transformations……Page 83
II Objects and Morphisms……Page 97
Objects and morphisms in abstract categories……Page 101
Objects and morphisms in concrete categories……Page 132
Injective objects and essential embeddings……Page 152
III Sources and Sinks……Page 166
Sources and sinks……Page 169
Limits and colimits……Page 193
Completeness and cocompleteness……Page 211
Functors and limits……Page 223
IV Factorization Structures……Page 235
Factorization structures for morphisms……Page 239
Factorization structures for sources……Page 257
E-reflective subcategories……Page 275
Factorization structures for functors……Page 290
V Adjoints and Monads……Page 301
Adjoint functors……Page 305
Adjoint situations……Page 315
Monads……Page 325
VI Topological and Algebraic Categories……Page 356
Topological categories……Page 359
Topological structure theorems……Page 382
Algebraic categories……Page 389
Algebraic structure theorems……Page 408
Topologically algebraic categories……Page 417
Topologically algebraic structure theorems……Page 429
VII Cartesian Closedness and Partial Morphisms……Page 434
Cartesian closed categories……Page 437
Partial morphisms, quasitopoi, and topological universes……Page 451
Bibliography……Page 469
Stability properties of special epimorphisms……Page 473
Table of Categories……Page 475
Table of Symbols……Page 480
Index……Page 484
GNU Free Documentation License……Page 518