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    Categories for the Working Mathematician (Graduate Texts in Mathematics) (Hardback) By (author) Saunders Mac Lane

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    DescriptionAn 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. It 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 characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.


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  • Full bibliographic data for Categories for the Working Mathematician

    Title
    Categories for the Working Mathematician
    Authors and contributors
    By (author) Saunders Mac Lane
    Physical properties
    Format: Hardback
    Number of pages: 329
    Width: 152 mm
    Height: 229 mm
    Thickness: 19 mm
    Weight: 642 g
    Language
    English
    ISBN
    ISBN 13: 9780387984032
    ISBN 10: 0387984038
    Classifications

    BIC E4L: MAT
    Nielsen BookScan Product Class 3: S7.8
    B&T Book Type: NF
    LC subject heading:
    B&T Merchandise Category: TXT
    B&T Modifier: Region of Publication: 01
    B&T General Subject: 710
    B&T Modifier: Continuations: 02
    B&T Modifier: Academic Level: 02
    Ingram Subject Code: MA
    Libri: I-MA
    BIC subject category V2: PBF, PBC
    Warengruppen-Systematik des deutschen Buchhandels: 16290
    BISAC V2.8: MAT018000
    DC21: 512.55
    LC subject heading:
    DC22: 512.55, 512/.55
    LC subject heading:
    BISAC V2.8: MAT012010
    B&T Approval Code: A51490000
    LC classification: QA169 .M33 1998, QA612.33, QA1-939
    Thema V1.0: PBF, PBC
    Edition
    2, Revised
    Edition statement
    2nd ed. 1978
    Illustrations note
    1, black & white illustrations
    Publisher
    Springer-Verlag New York Inc.
    Imprint name
    Springer-Verlag New York Inc.
    Publication date
    25 September 1998
    Publication City/Country
    New York, NY
    Review quote
    From the reviews of the second edition: "The book under review is an introduction to the theory of categories which, as the title suggests, is addressed to the (no-nonsense) working mathematician, thus presenting the ideas and concepts of Category Theory in a broad context of mainstream examples (primarily from algebra). ... the book remains an authoritative source on the foundations of the theory and an accessible first introduction to categories. ... It is very well-written, with plenty of interesting discussions and stimulating exercises." (Ittay Weiss, MAA Reviews, July, 2014) Second Edition S.M. Lane Categories for the Working Mathematician "A very useful introduction to category theory."-INTERNATIONALE MATHEMATISCHE NACHRICHTEN
    Table of contents
    1: Categories, Functors and Natural Transformation. 2: Constructions on Categories. 3: Universals and Limits. 4: Adjoints. 5: Limits. 6: Monads and Algebras. 7: Monoids. 8: Abelian Categories. 9: Special Limits. 10: Kan Extensions. 11: Symmetry and Braiding in Monoidal Categories. 12: Structures in Categories. Tables of Categories. Bibliography.