
Preface 
ix 

Preface to the second edition 
xi 

Preface to the third edition 
xii 




I. Introduction 
1 




II. Foundations 

1 
Sets, classes, and conglomerates 
9 




III. Categories 

2 
Concrete categories 
13 
3 
Abstract categories 
15 
4 
New categories from old 
23 




IV. Special Morphisms and Special Objects 

5 
Sections, retractions, and isomorphisms 
32 
6 
Monomorphisms, epimorphisms, and bimorphisms 
38 
7 
Initial, terminal, and zero objects 
46 
8 
Constant morphisms, zero morphisms, and pointed categories 
48 




V. Functors and Natural Transformations 

9 
Functors 
53 
10 
Homfunctors 
61 
11 
Categories of categories 
64 
12 
Properties of functors 
67 
13 
Natural transformations and natural isomorphisms 
77 
14 
Isomorphisms and equivalences of categories 
86 
15 
Functor categories 
93 




VI. Limits in Categories 

16 
Equalizers and coequalizers 
100 
17 
Intersections and factorizations 
107 
18 
Products and coproducts 
115 
19 
Sources and sinks 
126 
20 
Limits and colimits 
133 
21 
Pullbacks and pushouts 
138 
22 
Inverse and direct limits 
151 
23 
Complete categories 
155 
24 
Functors that preserve and reflect limits 
166 
25 
Limits in functor categories 
171 




VII. Adjoint Situations 

26 
Universal maps 
177 
27 
Adjoint functors 
194 
28 
Existence of adjoints 
207 




VIII. SetValued Functors 

29 
Homfunctors 
217 
30 
Representable functors 
221 
31 
Free objects 
231 
32 
Algebraic categories and algebraic functors 
236 




IX. Subobjects, Quotient Objects, and Factorizations 

33 
(E, M)Categories 
249 
34 
(Epi, extremal mono) and (extremal epi, mono) categories 
255 
35 
(Generating, extremal mono) and (extremal generating, mono) factorizations 
267 




X. Reflective Subcategories 

36 
General reflective subcategories 
275 
37 
Characterization and generation of Ereflective subcategories 
281 
38 
Algebraic subcategories 
288 




XI. Pointed Categories 

39 
Normal and exact categories 
294 
40 
Additive categories 
305 
41 
Abelian categories 
318 




Appendix: Foundations 
328 

Bibliography 
332 

Index of Symbols 
381 

Index 
383 