Overview

This up-to-date introductory treatment employs the language of category theory to explore the theory of structures. Its unique approach stresses concrete categories, and each categorical notion features several examples that clearly illustrate specific and general cases.A systematic view of factorization structures, this volume contains seven chapters. The first five focus on basic theory, and the final two explore more recent research results in the realm of concrete categories, cartesian closed categories, and quasitopoi. Suitable for advanced undergraduate and graduate students, it requires an elementary knowledge of set theory and can be used as a reference as well as a text. Updated by the authors in 2004, it offers a unifying perspective on earlier work and summarizes recent developments.

Full Product Details

Author:   Jiri Adamek (Czech Technical Univ., Prague) ,  Horst Herrlich ,  George E Strecker ,  Mathematics
Publisher:   Dover Publications Inc.
Imprint:   Dover Publications Inc.
Dimensions:   Width: 15.50cm , Height: 2.50cm , Length: 23.10cm
Weight:   0.658kg
ISBN:  

9780486469348

ISBN 10:   0486469344
Pages:   528
Publication Date:   01 July 2009
Audience:   General/trade ,  General
Format:   Paperback
Publisher's Status:   Out of Print
Availability:   Awaiting stock  

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

Reviews

Author Information

Jiri Adamek is affiliated with Prague's Charles University and the Academy of Sciences of the Czech Republic. Horst Herrlich is affiliated with the Department of Mathematics at the University of Bremen, Germany. George E. Strecker is a faculty member of the Department of Mathematics at Kansas State University.

Tab Content 6

Author Website:  

Countries Available

All regions