Format:
1 Online-Ressource (xii, 417 pages)
,
digital, PDF file(s).
ISBN:
9781107340985
,
9780521834148
Series Statement:
Encyclopedia of mathematics and its applications volume 97
Content:
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.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
,
Ordered sets via adjunction
,
Locales
,
Functional approach to general topology
,
Regular, protomodular, and Abelian categories
,
Aspects of monads
,
Algebraic categories
,
Sheaf theory
,
Beyond Barr exactness
Additional Edition:
ISBN 9780521834148
Additional Edition:
ISBN 9780521834148
Additional Edition:
Erscheint auch als Categorical foundations Cambridge [u.a.] : Cambridge University Press, 2004 ISBN 0521834147
Language:
English
Subjects:
Mathematics
Keywords:
Kategorie
DOI:
10.1017/CBO9781107340985
URL:
Volltext
(URL des Erstveröffentlichers)
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