
Contents  Prefaces (338 KB) 
ix 




I. Introduction (267 KB) 
1 




II. Foundations (131 KB) 

1 
Sets, classes, and conglomerates 
9 




III. Categories (604 KB) 

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




IV. Special Morphisms and Special Objects (686 KB) 

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 (1482 KB) 

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 (2286 KB) 

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 (1065 KB) 

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




VIII. SetValued Functors (1029 KB) 

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




IX. Subobjects, Quotient Objects, and Factorizations (716 KB) 

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 (628 KB) 

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




XI. Pointed Categories (966 KB) 

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




Foundations (125 KB) 
328 

Bibliography (2125 KB) 
332 

Index of Symbols (15 KB) 
381 

Corrections (9 KB) 
382 

Index (994 KB) 
383 