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Monoidal topology : = a categorical approach to order, metric and topology /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Monoidal topology :/ edited by Dirk Hofmann, Universidade de Aveiro, Swiss Federal Institute of Technology, Gavin J. Seal, Walter Tholen, York University, Toronto.
其他題名:	a categorical approach to order, metric and topology /
其他作者:	Hofmann, Dirk,
面頁冊數:	1 online resource (xvii, 503 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Topological semigroups. -
電子資源:	https://doi.org/10.1017/CBO9781107517288
ISBN:	9781107517288 (ebook)

Monoidal topology : = a categorical approach to order, metric and topology /
Monoidal topology :a categorical approach to order, metric and topology /edited by Dirk Hofmann, Universidade de Aveiro, Swiss Federal Institute of Technology, Gavin J. Seal, Walter Tholen, York University, Toronto. - 1 online resource (xvii, 503 pages) :digital, PDF file(s). - Encyclopedia of mathematics and its applications ;volume 153. - Encyclopedia of mathematics and its applications ;v. 82..

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.

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.

ISBN: 9781107517288 (ebook)Subjects--Topical Terms:

1239728
Topological semigroups.

LC Class. No.: QA387 / .M65 2014

Dewey Class. No.: 514/.32

Monoidal topology : = a categorical approach to order, metric and topology /
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a 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.
520 $a 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.
650 0 $a Topological semigroups. $3 1239728
650 0 $a Group theory. $3 527791
700 1 $a Hofmann, Dirk, $d 1970- $e editor. $3 1239725
700 1 $a Seal, Gavin J., $e editor. $3 1443373
700 1 $a Tholen, W. $q (Walter), $d 1947- $e editor. $3 1443374
776 0 8 $i Print version: $z 9781107063945
830 0 $a Encyclopedia of mathematics and its applications ; $v v. 82. $3 833009
856 4 0 $u https://doi.org/10.1017/CBO9781107517288