| Document Type
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BL
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| Record Number
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582979
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| Doc. No
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b412198
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| Main Entry
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Mac Lane, Saunders,1909-2005
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| Title & Author
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Categories for the working mathematician /\ Saunders Mac Lane
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| Edition Statement
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Second edition
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| Series Statement
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Graduate texts in mathematics ;; 5
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| Page. NO
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xii, 314 pages :: illustrations ;; 25 cm
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| ISBN
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0387984038 (hardcover : alk. paper)
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: 9780387984032 (hardcover : alk. paper)
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| Bibliographies/Indexes
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Includes bibliographical references (pages 297-302) and index
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| Contents
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I. Categories, Functors, and Natural Transformations -- II. Constructions on Categories -- III. Universals and Limits -- IV. Adjoints -- V. Limits -- VI. Monads and Algebras -- VII. Monoids -- VIII. Abelian Categories -- IX. Special Limits -- X. Kan Extensions -- XI. Symmetry and Braiding in Monoidal Categories -- XII. Structures in Categories -- App. Foundations -- Table of Standard Categories: Objects and Arrows
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| Abstract
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"Categories for the Working Mathematician provides an array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. The book then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterized by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions."--Jacket
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| Subject
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Categories (Mathematics)
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| Dewey Classification
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512/.55
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| LC Classification
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QA169.M33 1998
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