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Monoidal topologya categorical appro...

Hofmann, Dirk, (1970-)

Monoidal topologya categorical approach to order, metric and topology /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Monoidal topologyedited by Dirk Hofmann, Gavin J. Seal, Walter Tholen.
其他題名:	a categorical approach to order, metric and topology /
其他作者:	Hofmann, Dirk,
出版者:	Cambridge :Cambridge University Press,2014.
面頁冊數:	xvii, 503 p. :ill., digital ;24 cm.
標題:	Topological semigroups.
電子資源:	https://doi.org/10.1017/CBO9781107517288
ISBN:	9781107517288$q(electronic bk.)

Monoidal topologya categorical approach to order, metric and topology /
Monoidal topologya categorical approach to order, metric and topology /[electronic resource] :edited by Dirk Hofmann, Gavin J. Seal, Walter Tholen. - Cambridge :Cambridge University Press,2014. - xvii, 503 p. :ill., digital ;24 cm. - Encyclopedia of mathematics and its applications ;153. - Encyclopedia of mathematics and its applications ;v. 124-125..

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$q(electronic bk.)Subjects--Topical Terms:

844347
Topological semigroups.

LC Class. No.: QA387 / .M65 2014

Dewey Class. No.: 514.32

Monoidal topologya categorical approach to order, metric and topology /
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245 0 0 $a Monoidal topology $h [electronic resource] : $b a categorical approach to order, metric and topology / $c edited by Dirk Hofmann, Gavin J. Seal, Walter Tholen.
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300 $a xvii, 503 p. : $b ill., digital ; $c 24 cm.
490 1 $a Encyclopedia of mathematics and its applications ; $v 153
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 844347
650 0 $a Group theory. $3 189579
700 1 $a Hofmann, Dirk, $d 1970- $e editor $3 765826
700 1 $a Seal, Gavin J. $3 844345
700 1 $a Tholen, Walter, $d 1947- $e editor. $3 844346
830 0 $a Encyclopedia of mathematics and its applications ; $v v. 124-125. $3 403662
856 4 0 $u https://doi.org/10.1017/CBO9781107517288