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OverviewCategories 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 onsymmetric 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. Full Product DetailsAuthor: Saunders Mac LanePublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: 2nd ed. 1978. Softcover reprint of the original 2nd ed. 1978 Volume: 5 Dimensions: Width: 15.20cm , Height: 1.70cm , Length: 22.90cm Weight: 0.510kg ISBN: 9781441931238ISBN 10: 1441931236 Pages: 318 Publication Date: 19 November 2010 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of print, replaced by POD  We will order this item for you from a manufatured on demand supplier. Table of Contents1: 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.ReviewsSecond Edition S.M. Lane Categories for the Working Mathematician A very useful introduction to category theory. --INTERNATIONALE MATHEMATISCHE NACHRICHTEN Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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