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by Jiri Adamek,Horst Herrlich,George E Strecker
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ISBN: 0486469344 Dover Publications Price: $24.95 |
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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, offering a unifying perspective on earlier work and summarizing recent developments. Numerous examples, ranging from general to specific, illuminate the text. 1990 edition, updated 2004.
Reprint of the John Wiley & Sons, New York, 1990 edition, updated in 2004.
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Table of Contents for Abstract and Concrete Categories: The Joy of Cats
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