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Categorical Foundations: Special Topics in Order, Topology, Algebra, and Sheaf Theory - Couverture rigide

Livre 85 sur 188: Encyclopedia of Mathematics and its Applications
 
9780521834148: Categorical Foundations: Special Topics in Order, Topology, Algebra, and Sheaf Theory
Couverture rigide
ISBN 10 : 0521834147 ISBN 13 : 9780521834148
Editeur : Cambridge University Press, 2003

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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.

Revue de presse

'The book will be very useful for graduate students and teachers, and inspiring for the researchers interested in the discussed topics as well as in category theory itself.' EMS Newsletter

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Cambridge University Press
Date d'édition
2003
Langue
anglais
ISBN 10 
0521834147
ISBN 13 
9780521834148
Reliure
Relié
Nombre de pages
442
Éditeur
Pedicchio Maria Cristina, Tholen Walter
Coordonnées du fabricant
non disponible
Personne responsable
Avery
https://www.avery.fr/

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