ISBN-10:
0471609226
ISBN-13:
9780471609223
Pub. Date:
01/28/1990
Publisher:
Wiley
Abstract and Concrete Categories: The Joy of Cats / Edition 1

Abstract and Concrete Categories: The Joy of Cats / Edition 1

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Overview

A modern introduction to the theory of structures via the language of category theory. Unique to this book is the emphasis on concrete categories. Also noteworthy is the systematic treatment of factorization structures, which gives a new, unifying perspective to earlier work and summarizes recent developments. Each categorical notion is accompanied by many examples, usually moving from special cases to more general cases. Comprises seven chapters; the first five present the basic theory, while the last two contain more recent research results in the realm of concrete categories, cartesian closed categories and quasitopoi. The prerequisite is an elementary knowledge of set theory. Contains exercises.

Product Details

ISBN-13: 9780471609223
Publisher: Wiley
Publication date: 01/28/1990
Series: Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts Series , #6
Pages: 496
Product dimensions: 7.32(w) x 10.28(h) x 1.06(d)

Table of Contents

Motivation.

Foundations.

CATEGORIES, FUNCTORS, AND NATURAL TRANSFORMATIONS.

Categories and Functors.

Subcategories.

Concrete Categories and Concrete Functors.

Natural Transformations.

OBJECTS AND MORPHISMS.

Objects and Morphisms in Abstract Categories.

Objects and Morphisms in Concrete Categories.

Injective Objects and Essential Embeddings.

SOURCES AND SINKS.

Sources and Sinks.

Limits and Colimits.

Completeness and Cocompleteness.

Functors and Limits.

FACTORIZATION STRUCTURES.

Factorization Structures for Morphisms.

Factorization Structures for Sources.

E-Reflective Subcategories.

Factorization Structures for Functors.

ADJOINTS AND MONADS.

Adjoint Functors.

Adjoint Situations.

Monads.

TOPOLOGICAL AND ALGEBRAIC CATEGORIES.

Topological Categories.

Topological Structure Theorems.

Algebraic Categories.

Algebraic Structure Theorems.

Topologically Algebraic Categories.

Topologically Algebraic Structure Theorems.

CARTESIAN CLOSEDNESS AND PARTIAL MORPHISMS.

Cartesian Closed Categories.

Partial Morphisms, Quasitopoi, and Topological Universes.

Bibliography.

Tables.

Table of Categories.

Table of Symbols.

Index.

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