Categories for the Working MathematicianCategories 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 adjointlike 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 2categories 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  GoodreadsPart 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  GoodreadsHoly 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  165 
LXI  170 
LXII  174 
LXIII  175 
LXIV  180 
LXV  184 
XII  31 
XIII  33 
XIV  36 
XV  40 
XVI  42 
XVII  45 
XVIII  48 
XIX  51 
XX  55 
XXII  59 
XXIII  62 
XXIV  68 
XXV  72 
XXVI  75 
XXVII  76 
XXVIII  79 
XXIX  86 
XXX  90 
XXXI  92 
XXXII  95 
XXXIII  97 
XXXIV  99 
XXXV  103 
XXXVI  105 
XXXVII  106 
XXXVIII  109 
XL  112 
XLI  115 
XLII  116 
XLIII  118 
XLIV  120 
XLV  126 
XLVI  128 
XLVII  132 
XLVIII  137 
L  139 
LI  142 
LII  144 
LIII  147 
LIV  149 
LV  151 
LVI  156 
LXVI  185 
LXVII  188 
LXVIII  191 
LXX  194 
LXXI  198 
LXXII  202 
LXXIII  211 
LXXV  214 
LXXVI  217 
LXXVII  218 
LXXVIII  222 
LXXIX  226 
LXXX  228 
LXXXI  230 
LXXXII  233 
LXXXIV  235 
LXXXV  236 
LXXXVI  240 
LXXXVII  243 
LXXXVIII  245 
LXXXIX  248 
XC  251 
XCII  255 
XCIII  257 
XCIV  260 
XCV  263 
XCVI  266 
XCVII  267 
XCIX  270 
C  272 
CI  276 
CII  279 
CIII  281 
CIV  283 
CV  285 
CVI  289 
CVII  293 
CVIII  295 
CIX  297 
303  
Common terms and phrases
2category 2cells abelian category abelian groups adjoint functor adjoint functor theorem algebra arrow h assigns axioms bifunctor bijection binary biproduct braid called CGHaus codomain coend coequalizer colimits comma category commutative diagram construction continuous maps coproduct counit defined definition described dinatural domain dual elements equal equivalence exact sequences example Exercises exists factors finite products forgetful functor full subcategory functor category functor F given graph Hausdorff spaces hence homsets homomorphism homotopy identity arrow implies initial object inverse Kan extension kernel left adjoint Lemma limiting cone Mac Lane modules monad monic morphism natural isomorphism natural transformation operation pair of arrows parallel pair preorder preserves projections Proof Proposition prove pullback quotient Rmodule representation right adjoint right Kan extension ring simplicial small homsets small set smallcomplete strings subobjects subset Talgebras tensor product terminal object topological space unique arrow unit universal arrow usual vector space vertex
Popular passages
Page viii  CoSponsored by The Air Force Office of Scientific Research The Office of Naval Research The...