Monoidal topology: a categorical approach to order, metric and topology
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 co...
Saved in:
| Other Authors: | , , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2014
|
| Series: | Encyclopedia of mathematics and its applications
volume 153 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | 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 |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xvii, 503 pages) |
| ISBN: | 9781107517288 |
| DOI: | 10.1017/CBO9781107517288 |
Staff View
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| 245 | 1 | 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 |
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| 505 | 8 | |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 | ||
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| author_facet | Hofmann, Dirk 1970- Seal, Gavin J. Tholen, W. 1947- |
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| contents | 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 |
| ctrlnum | (ZDB-20-CBO)CR9781107517288 (OCoLC)894732766 (DE-599)BVBBV043941416 |
| dewey-full | 514/.32 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
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| dewey-search | 514/.32 |
| dewey-sort | 3514 232 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781107517288 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:15Z |
| institution | BVB |
| isbn | 9781107517288 |
| language | English |
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| series2 | Encyclopedia of mathematics and its applications |
| spelling | 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 Cambridge Cambridge University Press 2014 1 online resource (xvii, 503 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 153 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 Topological semigroups Group theory Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s Topologie (DE-588)4060425-1 s 1\p DE-604 Hofmann, Dirk 1970- edt Seal, Gavin J. edt Tholen, W. 1947- edt Erscheint auch als Druckausgabe 978-1-107-06394-5 https://doi.org/10.1017/CBO9781107517288 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Monoidal topology a categorical approach to order, metric and topology 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 Topological semigroups Group theory Gruppentheorie (DE-588)4072157-7 gnd Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4060425-1 |
| title | Monoidal topology a categorical approach to order, metric and topology |
| title_auth | Monoidal topology a categorical approach to order, metric and topology |
| title_exact_search | Monoidal topology a categorical approach to order, metric and topology |
| title_full | 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 |
| title_fullStr | 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 |
| title_full_unstemmed | 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 |
| title_short | Monoidal topology |
| title_sort | monoidal topology a categorical approach to order metric and topology |
| title_sub | a categorical approach to order, metric and topology |
| topic | Topological semigroups Group theory Gruppentheorie (DE-588)4072157-7 gnd Topologie (DE-588)4060425-1 gnd |
| topic_facet | Topological semigroups Group theory Gruppentheorie Topologie |
| url | https://doi.org/10.1017/CBO9781107517288 |
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