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Abstract and Concrete Categories: The Joy of Cats

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Abstract and Concrete Categories: The Joy of Cats Cover

 

Synopses & Reviews

Synopsis:

This up-to-date introductory treatment employs category theory to explore the theory of structures. Its unique approach stresses concrete categories and presents a systematic view of factorization structures. Numerous examples. 1990 edition, updated 2004.

Synopsis:

This up-to-date introductory treatment employs category theory to explore the theory of structures. Its unique approach stresses concrete categories and presents a systematic view of factorization structures. Numerous examples. 1990 edition, updated 2004.

Table of Contents

Preface to the 2004 Edition
 
Preface
 
0 Introduction

1 Motivation

2 Foundations

 
I Categories, Functors, and Natural Transformations

3 Categories and functors

4 Subcategories

5 Concrete categories and concrete functors

6 Natural transformations

 
II Objects and Morphisms

7 Objects and morphisms in abstract categories

8 Objects and morphisms in concrete categories

9 Injective objects and essential embeddings

 
III Sources and Sinks

10 Sources and sinks

11 Limits and colimits

12 Completeness and cocompleteness

13 Functors and limits

 
IV Factorization Structures

14 Factorization structures for morphisms

15 Factorization structures for sources

16 E-reflective subcategories

17 Factorization structures for functors

 
V Adjoints and Monads

18 Adjoint functors

19 Adjoint situations

20 Monads

 
VI Topological and Algebraic Categories

21 Topological categories

22 Topological structure theorems

23 Algebraic categories

24 Algebraic structure theorems

25 Topologically algebraic categories

26 Topologically algebraic structure theorems

 
VII Cartesian Closedness and Partial Morphisms

27 Cartesian closed categories

28 Partial morphisms, quasitopoi, and topological universes

 
Bibliography
 
Tables
Functors and morphisms: Preservation properties

Functors and morphisms: Reflection properties

Functors and limits

Functors and colimits

Stability properties of special epimorphisms

 
Table of Categories
 
Table of Symbols
 
Index

Product Details

ISBN:
9780486469348
Author:
Adamek, J.
Publisher:
Dover Publications
Author:
Strecker, George E
Author:
Mathematics
Author:
Adamek, Jiri
Author:
Herrlich, Horst
Subject:
Set Theory
Subject:
Categories (mathematics)
Subject:
Algebra - General
Subject:
Mathematics : Set Theory
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
20090731
Binding:
TRADE PAPER
Grade Level:
College/higher education:
Language:
English
Illustrations:
Y
Pages:
528
Dimensions:
9.25 x 6.13 in 1.5 lb

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Abstract and Concrete Categories: The Joy of Cats New Trade Paper
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Product details 528 pages Dover Publications - English 9780486469348 Reviews:
"Synopsis" by ,
This up-to-date introductory treatment employs category theory to explore the theory of structures. Its unique approach stresses concrete categories and presents a systematic view of factorization structures. Numerous examples. 1990 edition, updated 2004.
"Synopsis" by ,
This up-to-date introductory treatment employs category theory to explore the theory of structures. Its unique approach stresses concrete categories and presents a systematic view of factorization structures. Numerous examples. 1990 edition, updated 2004.
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