Aspects of algebraic exponentiation
We analyse some aspects of the notion of algebraic exponentiation introduced by the second author [16] and satisfied by the category Gp of groups. We show how this notion provides a new approach to the categorical-algebraic question of the centralization. We explore, in the category G p, the unusual...
Gespeichert in:
| Veröffentlicht in: | Bulletin of the Belgian Mathematical Society, Simon Stevin Simon Stevin, 2012-12, Vol.19 (5), p.823-844 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 844 |
|---|---|
| container_issue | 5 |
| container_start_page | 823 |
| container_title | Bulletin of the Belgian Mathematical Society, Simon Stevin |
| container_volume | 19 |
| creator | Bourn, Dominique Gray, James R.A |
| description | We analyse some aspects of the notion of algebraic exponentiation introduced by the second author [16] and satisfied by the category Gp of groups. We show how this notion provides a new approach to the categorical-algebraic question of the centralization. We explore, in the category G p, the unusual universal properties and constructions determined by this notion, and we show how it is the origin of various properties of this category. Key words and phrases : Fibration of points, Beck-Chevalley condition, centralizer, unital, Mal'cev and protomodular categories, locally cartesian closed category. |
| doi_str_mv | 10.36045/bbms/1354031552 |
| format | Article |
| fullrecord | <record><control><sourceid>gale_proje</sourceid><recordid>TN_cdi_projecteuclid_primary_oai_CULeuclid_euclid_bbms_1354031552</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A317588916</galeid><sourcerecordid>A317588916</sourcerecordid><originalsourceid>FETCH-LOGICAL-c410t-ad5d5b53fb654739ba04f28068a287347f51a94863ed36aead80b0ab3f371d7a3</originalsourceid><addsrcrecordid>eNptUE1LAzEUDKJgrd49Fnre9mVfsskel-IXFLzY8_KSTUrKfrFZQf-9qy2KKO8wMMwMM4-xWw4rzEDItTFNXHOUApBLmZ6xWQooEp4rOGczjgoSLoS4ZFcxHgBSzHI1Y8si9s6OcdH5BdV7ZwYKduHe-q517RhoDF17zS481dHdnHDOdvd3L5vHZPv88LQptokVHMaEKllJI9GbTAqFuSEQPtWQaUq1QqG85JQLnaGrMCNHlQYDZNCj4pUinLPimNsP3WEq5V5tHaqyH0JDw3vZUSg3u-2JPcHn6vJn9ZSxPGbsqXZlaH03DmSbEG1ZIFdS65xnk2r1j2q6yjXBTtN9mPhfBjga7NDFODj_3YpD-fX_P00-AOiqd4g</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Aspects of algebraic exponentiation</title><source>EZB-FREE-00999 freely available EZB journals</source><source>Project Euclid Complete</source><creator>Bourn, Dominique ; Gray, James R.A</creator><creatorcontrib>Bourn, Dominique ; Gray, James R.A</creatorcontrib><description>We analyse some aspects of the notion of algebraic exponentiation introduced by the second author [16] and satisfied by the category Gp of groups. We show how this notion provides a new approach to the categorical-algebraic question of the centralization. We explore, in the category G p, the unusual universal properties and constructions determined by this notion, and we show how it is the origin of various properties of this category. Key words and phrases : Fibration of points, Beck-Chevalley condition, centralizer, unital, Mal'cev and protomodular categories, locally cartesian closed category.</description><identifier>ISSN: 1370-1444</identifier><identifier>EISSN: 2034-1970</identifier><identifier>DOI: 10.36045/bbms/1354031552</identifier><language>eng</language><publisher>Belgian Mathematical Society</publisher><subject>13A99 ; 17B99 ; 18A40 ; 18C15 ; 18D15 ; 20A05 ; Beck-Chevalley condition ; centralizer ; Fibration of points ; Functional equations ; Functions ; Group theory ; locally cartesian closed category ; Mal'cev and protomodular categories ; Theorems (Mathematics) ; unital</subject><ispartof>Bulletin of the Belgian Mathematical Society, Simon Stevin, 2012-12, Vol.19 (5), p.823-844</ispartof><rights>COPYRIGHT 2012 Belgian Mathematical Society</rights><rights>Copyright 2012 The Belgian Mathematic Society</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c410t-ad5d5b53fb654739ba04f28068a287347f51a94863ed36aead80b0ab3f371d7a3</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,776,780,881,921,27901,27902</link.rule.ids></links><search><creatorcontrib>Bourn, Dominique</creatorcontrib><creatorcontrib>Gray, James R.A</creatorcontrib><title>Aspects of algebraic exponentiation</title><title>Bulletin of the Belgian Mathematical Society, Simon Stevin</title><description>We analyse some aspects of the notion of algebraic exponentiation introduced by the second author [16] and satisfied by the category Gp of groups. We show how this notion provides a new approach to the categorical-algebraic question of the centralization. We explore, in the category G p, the unusual universal properties and constructions determined by this notion, and we show how it is the origin of various properties of this category. Key words and phrases : Fibration of points, Beck-Chevalley condition, centralizer, unital, Mal'cev and protomodular categories, locally cartesian closed category.</description><subject>13A99</subject><subject>17B99</subject><subject>18A40</subject><subject>18C15</subject><subject>18D15</subject><subject>20A05</subject><subject>Beck-Chevalley condition</subject><subject>centralizer</subject><subject>Fibration of points</subject><subject>Functional equations</subject><subject>Functions</subject><subject>Group theory</subject><subject>locally cartesian closed category</subject><subject>Mal'cev and protomodular categories</subject><subject>Theorems (Mathematics)</subject><subject>unital</subject><issn>1370-1444</issn><issn>2034-1970</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNptUE1LAzEUDKJgrd49Fnre9mVfsskel-IXFLzY8_KSTUrKfrFZQf-9qy2KKO8wMMwMM4-xWw4rzEDItTFNXHOUApBLmZ6xWQooEp4rOGczjgoSLoS4ZFcxHgBSzHI1Y8si9s6OcdH5BdV7ZwYKduHe-q517RhoDF17zS481dHdnHDOdvd3L5vHZPv88LQptokVHMaEKllJI9GbTAqFuSEQPtWQaUq1QqG85JQLnaGrMCNHlQYDZNCj4pUinLPimNsP3WEq5V5tHaqyH0JDw3vZUSg3u-2JPcHn6vJn9ZSxPGbsqXZlaH03DmSbEG1ZIFdS65xnk2r1j2q6yjXBTtN9mPhfBjga7NDFODj_3YpD-fX_P00-AOiqd4g</recordid><startdate>20121201</startdate><enddate>20121201</enddate><creator>Bourn, Dominique</creator><creator>Gray, James R.A</creator><general>Belgian Mathematical Society</general><general>The Belgian Mathematical Society</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20121201</creationdate><title>Aspects of algebraic exponentiation</title><author>Bourn, Dominique ; Gray, James R.A</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c410t-ad5d5b53fb654739ba04f28068a287347f51a94863ed36aead80b0ab3f371d7a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>13A99</topic><topic>17B99</topic><topic>18A40</topic><topic>18C15</topic><topic>18D15</topic><topic>20A05</topic><topic>Beck-Chevalley condition</topic><topic>centralizer</topic><topic>Fibration of points</topic><topic>Functional equations</topic><topic>Functions</topic><topic>Group theory</topic><topic>locally cartesian closed category</topic><topic>Mal'cev and protomodular categories</topic><topic>Theorems (Mathematics)</topic><topic>unital</topic><toplevel>online_resources</toplevel><creatorcontrib>Bourn, Dominique</creatorcontrib><creatorcontrib>Gray, James R.A</creatorcontrib><collection>CrossRef</collection><jtitle>Bulletin of the Belgian Mathematical Society, Simon Stevin</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bourn, Dominique</au><au>Gray, James R.A</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Aspects of algebraic exponentiation</atitle><jtitle>Bulletin of the Belgian Mathematical Society, Simon Stevin</jtitle><date>2012-12-01</date><risdate>2012</risdate><volume>19</volume><issue>5</issue><spage>823</spage><epage>844</epage><pages>823-844</pages><issn>1370-1444</issn><eissn>2034-1970</eissn><abstract>We analyse some aspects of the notion of algebraic exponentiation introduced by the second author [16] and satisfied by the category Gp of groups. We show how this notion provides a new approach to the categorical-algebraic question of the centralization. We explore, in the category G p, the unusual universal properties and constructions determined by this notion, and we show how it is the origin of various properties of this category. Key words and phrases : Fibration of points, Beck-Chevalley condition, centralizer, unital, Mal'cev and protomodular categories, locally cartesian closed category.</abstract><pub>Belgian Mathematical Society</pub><doi>10.36045/bbms/1354031552</doi><tpages>24</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1370-1444 |
| ispartof | Bulletin of the Belgian Mathematical Society, Simon Stevin, 2012-12, Vol.19 (5), p.823-844 |
| issn | 1370-1444 2034-1970 |
| language | eng |
| recordid | cdi_projecteuclid_primary_oai_CULeuclid_euclid_bbms_1354031552 |
| source | EZB-FREE-00999 freely available EZB journals; Project Euclid Complete |
| subjects | 13A99 17B99 18A40 18C15 18D15 20A05 Beck-Chevalley condition centralizer Fibration of points Functional equations Functions Group theory locally cartesian closed category Mal'cev and protomodular categories Theorems (Mathematics) unital |
| title | Aspects of algebraic exponentiation |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-10T10%3A31%3A16IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-gale_proje&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Aspects%20of%20algebraic%20exponentiation&rft.jtitle=Bulletin%20of%20the%20Belgian%20Mathematical%20Society,%20Simon%20Stevin&rft.au=Bourn,%20Dominique&rft.date=2012-12-01&rft.volume=19&rft.issue=5&rft.spage=823&rft.epage=844&rft.pages=823-844&rft.issn=1370-1444&rft.eissn=2034-1970&rft_id=info:doi/10.36045/bbms/1354031552&rft_dat=%3Cgale_proje%3EA317588916%3C/gale_proje%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_galeid=A317588916&rfr_iscdi=true |