Category Theory ( Oxford Logic Guides #52 ) (2ND)

基本信息

Series:Oxford Logic Guides

Format:Paperback / softback 336 pages

Publisher:Oxford University Press

Imprint:Oxford University Press

Edition:2 Revised edition

ISBN:9780199237180

Published:17 Jun 2010

Classifications:Philosophy: logic, Philosophy of mathematics, Mathematical logic, Functional analysis & transforms

Readership:Postgraduate, Research & Scholarly

Weight:492g

Dimensions:233 x 156 x 19 (mm)

頁面參數僅供參考，具體以實物為準

書籍簡介

範疇理論是抽象代數的一個分支，其應用極為廣泛。這篇文章和參考書不僅針對數學家，但也研究人員和學生的計算機科學，邏輯，語言學，認知科學，哲學，和任何其他領域的想法正在被應用。包含了基本概念的明確定義，闡明瞭大量的例子，並提供了所有重要的命題和定理的充分證明，這本書的目的是使基本的思想，定理，和方法的範疇理論可以理解的廣大讀者。

雖然數學的前提條件很少，數學嚴謹的標準就不會打折扣。涵蓋的材料包括類別的標準核心;仿函數;自然的轉換;等價;限制和colimits;函子類別;能被描繪的;Yoneda引理;伴隨;單體。另外還提供了一個關於笛卡爾封閉範疇和lambada -calculus的話題——這是計算機科學家、邏輯學家和語言學家的必修課!

這第二版包含了對原始文本的許多修訂，包括擴展闡述，修訂和詳細的證明，提供額外的圖表，糾正排印錯誤，最後，增加了一個關於單線類的全新部分。還增加了近百個新的練習，許多都有解答，使這本書更有用的課程文本和自學。

Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied. 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 assuming 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!

This Second Edition contains numerous revisions to the original text, including expanding the exposition, revising and elaborating the proofs, providing additional diagrams, correcting typographical errors and, finally, adding an entirely new section on monoidal categories. Nearly a hundred new exercises have also been added, many with solutions, to make the book more useful as a course text and for self-study.

目錄

Preface

1. Categories

2. Abstract Structures

3. Duality

4. Groups and Categories

5. Limits and Colimits

6. Exponentials

7. Naturality

8. Categories of Diagrams

9. Adjoints

10. Monads and Algrebras

References

Solutions to Selected Exercises

Index

作者簡介

Steve Awodey在馬爾堡大學(德國)和芝加哥大學學習數學和哲學，1997年在芝加哥大學獲得桑德斯·麥克·萊恩博士學位。他現在是卡內基梅隆大學哲學系的教授。他是範疇理論和邏輯方面的活躍研究者，並撰寫和合作撰寫了許多期刊文章。

Steve Awodey studied Mathematics and Philosophy at the University of Marburg (Germany) and the University of Chicago, earning his Ph.D. from Chicago under Saunders Mac Lane in 1997. He is now a Professor in the Department of Philosophy at Carnegie Mellon University. He is an active researcher in Category Theory and Logic, and has authored and co-authored numerous journal articles.