# Categorical Closure Operators

• Gabriele Castellini
Book

Part of the Mathematics: Theory & Applications book series (MTA)

## Table of contents

1. Front Matter
Pages i-xii
2. ### General Theory

1. Front Matter
Pages 1-1
2. Gabriele Castellini
Pages 3-8
3. Gabriele Castellini
Pages 9-24
4. Gabriele Castellini
Pages 25-40
5. Gabriele Castellini
Pages 41-56
6. Gabriele Castellini
Pages 57-63
7. Gabriele Castellini
Pages 65-79
8. Gabriele Castellini
Pages 81-93
9. Gabriele Castellini
Pages 95-108
10. Gabriele Castellini
Pages 109-122
11. Gabriele Castellini
Pages 123-127
3. ### Applications

1. Front Matter
Pages 129-129
2. Gabriele Castellini
Pages 131-135
3. Gabriele Castellini
Pages 137-163
4. Gabriele Castellini
Pages 165-196
5. Gabriele Castellini
Pages 197-229
6. Gabriele Castellini
Pages 231-253
7. Gabriele Castellini
Pages 255-270
8. Gabriele Castellini
Pages 271-277

## About this book

### Introduction

This book presents the general theory of categorical closure operators to­ gether with a number of examples, mostly drawn from topology and alge­ bra, which illustrate the general concepts in several concrete situations. It is aimed mainly at researchers and graduate students in the area of cate­ gorical topology, and to those interested in categorical methods applied to the most common concrete categories. Categorical Closure Operators is self-contained and can be considered as a graduate level textbook for topics courses in algebra, topology or category theory. The reader is expected to have some basic knowledge of algebra, topology and category theory, however, all categorical concepts that are recurrent are included in Chapter 2. Moreover, Chapter 1 contains all the needed results about Galois connections, and Chapter 3 presents the the­ ory of factorization structures for sinks. These factorizations not only are essential for the theory developed in this book, but details about them can­ not be found anywhere else, since all the results about these factorizations are usually treated as the duals of the theory of factorization structures for sources. Here, those hard-to-find details are provided. Throughout the book I have kept the number of assumptions to a min­ imum, even though this implies that different chapters may use different hypotheses. Normally, the hypotheses in use are specified at the beginning of each chapter and they also apply to the exercise set of that chapter.

### Keywords

Abelian group Boundary value problem Category theory algebra terminal object topology

#### Authors and affiliations

• Gabriele Castellini
• 1
1. 1.Department of Mathematics MayaguezUniversity of Puerto RicoPuerto RicoUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-0-8176-8234-7
• Copyright Information Birkhäuser Boston 2003
• Publisher Name Birkhäuser, Boston, MA
• eBook Packages
• Print ISBN 978-1-4612-6504-7
• Online ISBN 978-0-8176-8234-7
• About this book