UID:
almafu_9960117384502883
Format:
1 online resource (xvii, 503 pages) :
,
digital, PDF file(s).
ISBN:
1-139-98636-8
,
1-139-99099-3
,
1-316-01157-7
,
1-316-01381-2
,
1-107-51728-1
,
1-316-00257-8
,
1-316-00707-3
,
1-316-00481-3
,
1-316-00931-9
Series Statement:
Encyclopedia of mathematics and its applications ; volume 153
Content:
Monoidal Topology describes an active research area that, after various past proposals on how to axiomatize 'spaces' in terms of convergence, began to emerge at the beginning of the millennium. It combines Barr's relational presentation of topological spaces in terms of ultrafilter convergence with Lawvere's interpretation of metric spaces as small categories enriched over the extended real half-line. Hence, equipped with a quantale V (replacing the reals) and a monad T (replacing the ultrafilter monad) laxly extended from set maps to V-valued relations, the book develops a categorical theory of (T,V)-algebras that is inspired simultaneously by its metric and topological roots. The book highlights in particular the distinguished role of equationally defined structures within the given lax-algebraic context and presents numerous new results ranging from topology and approach theory to domain theory. All the necessary pre-requisites in order and category theory are presented in the book.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
Introduction / Robert Lowen and Walter Tholen -- Monoidal structures / Gavin J. Seal and Walter Tholen -- Lax algebras / Dirk Hofmann, Gavin J. Seal, and Walter Tholen -- Kleisli monoids / Dirk Hofmann, Robert Lowen, Rory Lucyshyn-Wright, and Gavin J. Seal -- Lax algebras as spaces / Maria Manuel Clementino, Eva Colebunders, and Walter Tholen.
,
English
Additional Edition:
ISBN 1-322-06689-2
Additional Edition:
ISBN 1-107-06394-9
Language:
English
URL:
https://doi.org/10.1017/CBO9781107517288
