Categories for the Working Mathematician

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Springer Science & Business Media, Sep 25, 1998 - Mathematics - 314 pages
5 Reviews
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. This second edition includes a number of revisions and additions, including two new chapters on topics of active interest. One is on symmetric monoidal categories and braided monoidal categories and the coherence theorems for them. The second describes 2-categories and the higher dimensional categories which have recently come into prominence. The bibliography has also been expanded to cover some of the many other recent advances concerning categories.
  

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Review: Categories for the Working Mathematician (Graduate Texts in Mathematics #5)

User Review  - Tyler Weir - Goodreads

Part of the RedditU course on Category Theory. Read full review

Review: Categories for the Working Mathematician (Graduate Texts in Mathematics #5)

User Review  - Steve Miller - Goodreads

Holy Crap! Everything you ever wanted to know about category theory in one astoundingly clear and concise book. This is truly one stop shopping for category theorists and it has been a good friend ... Read full review

Contents

IV
7
V
10
VI
13
VII
16
VIII
19
IX
21
X
24
XI
27
LVII
157
LVIII
161
LX
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LXI
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LXII
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LXIII
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LXIV
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LXV
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XII
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XIII
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XIV
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XV
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XVI
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XVII
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XVIII
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XIX
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XX
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XXII
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XXIII
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XXIV
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XXV
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XXVI
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XXVII
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XXVIII
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XXIX
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XXX
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XXXI
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XXXII
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XXXIII
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XXXIV
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XXXV
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XXXVI
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XXXVII
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XXXVIII
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XL
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XLI
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XLII
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XLIII
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XLIV
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XLV
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XLVI
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XLVII
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XLVIII
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L
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LI
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LII
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LIII
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LIV
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LV
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LVI
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LXVI
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LXVII
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LXVIII
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LXX
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LXXI
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LXXII
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LXXIII
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LXXV
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LXXVI
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LXXVII
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LXXVIII
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LXXIX
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LXXX
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LXXXI
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LXXXII
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LXXXIV
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LXXXV
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LXXXVI
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LXXXVII
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LXXXVIII
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LXXXIX
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XC
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XCII
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XCIII
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XCIV
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XCV
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XCVI
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XCVII
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XCIX
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C
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CI
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CII
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CIII
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CIV
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CV
285
CVI
289
CVII
293
CVIII
295
CIX
297
CX
303
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About the author (1998)

Biography of Saunders Mac Lane

Saunders Mac Lane was born on August 4, 1909 in Connecticut. He studied at Yale University and then at the University of Chicago and at Gttingen, where he received the D.Phil. in 1934. He has tought at Harvard, Cornell and the University of Chicago.

Mac Lane's initial research was in logic and in algebraic number theory (valuation theory). With Samuel Eilenberg he published fifteen papers on algebraic topology. A number of them involved the initial steps in the cohomology of groups and in other aspects of homological algebra - as well as the discovery of category theory. His famous and undergraduate textbook Survey of modern algebra, written jointly with G. Birkhoff, has remained in print for over 50 years. Mac Lane is also the author of several other highly successful books.

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