大葉大學圖書館 |

Monoidal topology[electronic resource] :a categorical approach to order, metric and topology /

紀錄類型:	書目-電子資源 : Monograph/item
杜威分類號:	514.32
書名/作者:	Monoidal topology : a categorical approach to order, metric and topology // edited by Dirk Hofmann, Gavin J. Seal, Walter Tholen.
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.
標題:	Group theory.
ISBN:	9781107517288
ISBN:	9781107063945
內容註:	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.
摘要、提要註:	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.
電子資源:	https://doi.org/10.1017/CBO9781107517288

Monoidal topology[electronic resource] :a 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. 143..

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: 9781107517288Subjects--Topical Terms:

711894
Topological semigroups.

LC Class. No.: QA387 / .M65 2014

Dewey Class. No.: 514.32

Monoidal topology[electronic resource] :a categorical approach to order, metric and topology /
LDR:02227nmm a2200265 a 4500 001 491957
003 UkCbUP
005 20151005020621.0
006 m d
007 cr nn 008maaau
008 210201s2014 enk o 1 0 eng d
020 $a 9781107517288 $q (electronic bk.)
020 $a 9781107063945 $q (paper)
035 $a CR9781107517288
040 $a UkCbUP $b eng $c UkCbUP $d GP
041 0 $a eng
050 4 $a QA387 $b .M65 2014
082 0 4 $a 514.32 $2 23
090 $a QA387 $b .M751 2014
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.
260 $a Cambridge : $b Cambridge University Press, $c 2014.
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 711894
650 0 $a Group theory. $3 404655
700 1 $a Hofmann, Dirk, $d 1970- $e editor. $3 711891
700 1 $a Seal, Gavin J. $3 711892
700 1 $a Tholen, Walter, $d 1947- $e editor. $3 711893
830 0 $a Encyclopedia of mathematics and its applications ; $v v. 143. $3 641511
856 4 0 $u https://doi.org/10.1017/CBO9781107517288