國立虎尾科技大學 |

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

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Monoidal topology :/ edited by Dirk Hofmann, Universidade de Aveiro, Swiss Federal Institute of Technology, Gavin J. Seal, Walter Tholen, York University, Toronto.
Reminder of title:	a categorical approach to order, metric and topology /
other author:	Tholen, W.
Description:	1 online resource (xvii, 503 pages) :digital, PDF file(s). :
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Group theory. -
Online resource:	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:

527791
Group theory.

LC Class. No.: QA387 / .M65 2014

Dewey Class. No.: 514/.32

Monoidal topology : = a categorical approach to order, metric and topology /
LDR:02546nam a2200301 i 4500 001 1125261
003 UkCbUP
005 20151005020621.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 240926s2014||||enk o ||1 0|eng|d
020 $a 9781107517288 (ebook)
020 $z 9781107063945 (hardback)
035 $a CR9781107517288
040 $a UkCbUP $b eng $e rda $c UkCbUP
050 0 0 $a QA387 $b .M65 2014
082 0 0 $a 514/.32 $2 23
245 0 0 $a Monoidal topology : $b a categorical approach to order, metric and topology / $c edited by Dirk Hofmann, Universidade de Aveiro, Swiss Federal Institute of Technology, Gavin J. Seal, Walter Tholen, York University, Toronto.
264 1 $a Cambridge : $b Cambridge University Press, $c 2014.
300 $a 1 online resource (xvii, 503 pages) : $b digital, PDF file(s).
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
490 1 $a Encyclopedia of mathematics and its applications ; $v volume 153
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 Group theory. $3 527791
650 0 $a Topological semigroups. $3 1239728
700 1 $a Tholen, W. $q (Walter), $d 1947- $e editor. $3 1443374
700 1 $a Seal, Gavin J., $e editor. $3 1443373
700 1 $a Hofmann, Dirk, $d 1970- $e editor. $3 1239725
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