Categories for the Working Mathematician

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Beschreibung

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 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.

Zusammenfassung

This new edition of Categories for the Working Mathematician 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.

Inhaltsverzeichnis

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.

Erscheinungsjahr:	2010
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	332
Reihe:	Graduate Texts in Mathematics
Inhalt:	xii 318 S. 8 s/w Illustr.
ISBN-13:	9781441931238
ISBN-10:	1441931236
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Mac Lane, Saunders
Auflage:	2nd ed. 1978. Softcover reprint of the original 2nd ed. 1978
Hersteller:	Springer US Springer New York Graduate Texts in Mathematics
Maße:	229 x 152 x 19 mm
Von/Mit:	Saunders Mac Lane
Erscheinungsdatum:	19.11.2010
Gewicht:	0,482 kg

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