Categorical foundations

Special topics in order, topology, algebra, and sheaf theory

Maria Cristina Pedicchio, Walter Tholen

440 pages, parution le 15/01/2004

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Résumé

The book offers categorical introductions to order, topology, algebra and sheaf theory, suitable for graduate students, teachers and researchers of pure mathematics. Readers familiar with the very basic notions of category theory will learn about the main tools that are used in modern categorical mathematics but are not readily available in the literature. Hence, in eight rather independent chapters the reader will encounter various ways of how to study 'spaces': order-theoretically via their open-set lattices, as objects of a fairly abstract category merely via their interaction with other objects, or via their topoi of set-valued sheaves. Likewise, 'algebras' are treated both as models for Lawvere's algebraic theories and as Eilenberg-Moore algebras for monads, but they appear also as the objects of an abstract category with various levels of 'exactness' conditions. The abstract methods are illustrated by applications which, in many cases, lead to results not yet found in more traditional presentations of the various subjects, for instance on the exponentiability of spaces and embeddability of algebras. Suggestions for further studies and research are also given.

Sommaire

Introduction Walter Tholen
Ordered sets via adjunction R. J. Wood
Locales Jorge Picado, Ales Pultr and Anna Tozzi
A functional approach to general topology Maria Manuel Clementino, Eraldo Giuli and Walter Tholen
Regular, protomodular and abelian categories Dominique Bourn and Marino Gran
Aspects of monads John MacDonald and Manuela Sobral
Algebraic categories Maria Cristina Pedicchio and Fabrizio Rovatti
Sheaf theory Claudia Centazzo and Enrico M. Vitale
Beyond barr exactness: effective descent morphisms George Janelidze, Manuela Sobral and Walter Tholen.

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Maria Cristina Pedicchio, Walter Tholen
Parution	15/01/2004
Nb. de pages	440
Format	16,5 x 24
Couverture	Relié
Poids	769g
Intérieur	Noir et Blanc
EAN13	9780521834148
ISBN13	978-0-521-83414-8