範疇論 Category Theory (Oxford Logic Guides)

Awodey, Steve

Clarendon Press（2006/05発売）

• 製本 Hardcover:ハードカバー版／ページ数 270 p.／サイズ 298 b/w line drawings
• 言語 ENG
• 商品コード 9780198568612
• DDC分類 512.62

基本説明

This text provides a comprehensive reference to category theory, containing exercises, for researchers and graduates in philosophy, mathematics, computer science, logic and cognitive science. The basic definitions, theorems, and proofs are made accessible by assuming few mathematical pre-requisites but without compromising mathematical rigour.

Full Description

This text and reference book on Category Theory, a branch of abstract algebra, is aimed not only at students of Mathematics, but also researchers and students of Computer Science, Logic, Linguistics, Cognitive Science, Philosophy, and any of the other fields that now make use of it. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of Category Theory understandable to this broad readership. Although it assumes few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided; a must for computer scientists, logicians and linguists!

Contents

Preface; 1. Categories; 2. Abstract structures; 3. Duality; 4. Groups and categories; 5. Limits and colimits; 6. Exponentials; 7. Functors and Naturality; 8. Categories of Diagrams; 9. Adjoints; 10. Monads and algebras; References; Index