Abstract and Concrete Categories: The Joy of Cats

Publisher:

Dover Publications

Publication Date:

2009

Number of Pages:

517

Format:

Paperback

Price:

24.95

ISBN:

9780486469348

Category:

Monograph

We do not plan to review this book.

Preface to the 2004 Edition

Preface

0 Introduction
1 Motivation
2 Foundations

I Categories, Functors, and Natural Transformations
3 Categories and functors
4 Subcategories
5 Concrete categories and concrete functors
6 Natural transformations

II Objects and Morphisms
7 Objects and morphisms in abstract categories
8 Objects and morphisms in concrete categories
9 Injective objects and essential embeddings

III Sources and Sinks
10 Sources and sinks
11 Limits and colimits
12 Completeness and cocompleteness
13 Functors and limits

IV Factorization Structures
14 Factorization structures for morphisms
15 Factorization structures for sources
16 E-reflective subcategories
17 Factorization structures for functors

V Adjoints and Monads
18 Adjoint functors
19 Adjoint situations
20 Monads

VI Topological and Algebraic Categories
21 Topological categories
22 Topological structure theorems
23 Algebraic categories
24 Algebraic structure theorems
25 Topologically algebraic categories
26 Topologically algebraic structure theorems

VII Cartesian Closedness and Partial Morphisms
27 Cartesian closed categories
28 Partial morphisms, quasitopoi, and topological universes

Bibliography

Tables
Functors and morphisms: Preservation properties
Functors and morphisms: Reflection properties
Functors and limits
Functors and colimits
Stability properties of special epimorphisms

Table of Categories

Table of Symbols

Index