SSPM
Vol 1
Catalogue of
Book Series
List of Books
in this Series
Next Book
in this Series
Sigma Series in Pure Mathematics -- Volume 1
Enlarged Picture
Horst Herrlich, George E. Strecker
Category Theory. Third Edition
xvi+402 pages, free electronic publication, ISBN 978-3-88538-001-6, 2007
This is a by now classical text in mathematics. It gives an introduction
to category theory assuming only minimal knowledge in set theory, algebra
or topology. The book is designed for use during the early stages of graduate
study -- or for ambitious undergraduates. Each chapter contains numerous
exercises for further study and control.
The attempt is made to present category theory mainly as a convenient language
-- one which ties together widespread notions, which puts many existing results
in their proper perspective, and which provides a means for appreciation of the
unity that exists in modern mathematics, despite the increasing tendencies toward
fragmentation and specialization.
The fact that the book appears in a 3rd edition proves that the authors achieved
their goals.
The more advanced book "Abstract and Concrete Categories",
which the authors of this book wrote together with Jiri Adamek, is also available from Heldermann
Verlag as a free electronic publication.
Contents for Downloading:
1
Sets, classes, and conglomerates
9
2
Concrete categories
13
3
Abstract categories
15
4
New categories from old
23
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
9
Functors
53
10
Hom-functors
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
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
26
Universal maps
177
27
Adjoint functors
194
28
Existence of adjoints
207
29
Hom-functors
217
30
Representable functors
221
31
Free objects
231
32
Algebraic categories and algebraic functors
236
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
36
General reflective subcategories
275
37
Characterization and generation of E-reflective subcategories
281
38
Algebraic subcategories
288
39
Normal and exact categories
294
40
Additive categories
305
41
Abelian categories
318
Horst Herrlich was professor of mathematics at the University of Bremen, Germany.