Articoli correlati a Categories for the Working Mathematician
Sinossi
Saunders MacLane, born in Connecticut in 1909, studied mathematics at Yale, Chicago and Göttingen and has taught mathematics at Harvard, Cornell and the University of Chicago. He is now the Max Mason Distinguished Service Professor of Mathematics at the University of Chicago. With Samuel Eilenberg he discovered the theory of categories and some of the basic ideas of homological algebra. His book Homology, covering the latter subject, was published by Springer-Verlag in 1963. This book summarizes the ideas and methods of category theory, which can now be effectively used by mathematicians working in a variety of other fields of mathematical research. The book is based on his lectures at Chicago, Canberra, Bowdoin and Tulane.
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Contenuti
Contents: Categories, Functors and Natural Transformations.- Constructions on Categories.- Universals and Limits.- Adjoints.- Limits.- Monads and Algebras.- Monoids.- Abelian Categories.- Special Limits.- Kan Extensions.- Table of Terminology.- Bibliography.- Index.
Product Description
Book by Saunders Mac Lane
Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.
- EditoreSpringer
- Data di pubblicazione1994
- ISBN 10 0387900357
- ISBN 13 9780387900353
- RilegaturaCopertina rigida
- Numero edizione1
- Numero di pagine271
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Categories for the Working Mathematician
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Hardcover. Condizione: Good. 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. 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. Codice articolo AMPLE0387900357
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