The canonical intensive quality of a cohesive topos

Autores
Marmolejo, Francisco; Menni, Matías
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We strengthen a result of Lawvere by proving that every pre-cohesive geometric morphism p: E --> S has a canonical intensive quality s: E --> L. We also discuss examples among bounded pre-cohesive p: E --> S and, in particular, we show that if E is a presheaf topos then so is L.This result lifts to Grothendieck toposes but the sites obtained need not be subcanonical.To illustrate this phenomenon, and also the subtle passage from E to L,we consider a particular family of bounded cohesive toposes over Set and build subcanonical sites fortheir associated categories L.
Fil: Marmolejo, Francisco. Universidad Nacional Autónoma de México; México
Fil: Menni, Matías. Universidad Nacional de La Plata. Facultad de Informática. Laboratorio de Investigación y Formación en Informática Avanzada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
Materia
Topos Theory
Axiomatic Cohesion
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/164666
Acceder
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network_name_str CONICET Digital (CONICET)
spelling The canonical intensive quality of a cohesive toposMarmolejo, FranciscoMenni, MatíasTopos TheoryAxiomatic Cohesionhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We strengthen a result of Lawvere by proving that every pre-cohesive geometric morphism p: E --> S has a canonical intensive quality s: E --> L. We also discuss examples among bounded pre-cohesive p: E --> S and, in particular, we show that if E is a presheaf topos then so is L.This result lifts to Grothendieck toposes but the sites obtained need not be subcanonical.To illustrate this phenomenon, and also the subtle passage from E to L,we consider a particular family of bounded cohesive toposes over Set and build subcanonical sites fortheir associated categories L.Fil: Marmolejo, Francisco. Universidad Nacional Autónoma de México; MéxicoFil: Menni, Matías. Universidad Nacional de La Plata. Facultad de Informática. Laboratorio de Investigación y Formación en Informática Avanzada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaTheory And Applications Of Categories2021-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/164666Marmolejo, Francisco; Menni, Matías; The canonical intensive quality of a cohesive topos; Theory And Applications Of Categories; Theory And Applications Of Categories; 36; 9; 10-2021; 250-2791201-561XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.tac.mta.ca/tac/volumes/36/9/36-09abs.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T09:53:31Zoai:ri.conicet.gov.ar:11336/164666instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-11-05 09:53:31.45CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The canonical intensive quality of a cohesive topos
title The canonical intensive quality of a cohesive topos
spellingShingle The canonical intensive quality of a cohesive topos
Marmolejo, Francisco
Topos Theory
Axiomatic Cohesion
title_short The canonical intensive quality of a cohesive topos
title_full The canonical intensive quality of a cohesive topos
title_fullStr The canonical intensive quality of a cohesive topos
title_full_unstemmed The canonical intensive quality of a cohesive topos
title_sort The canonical intensive quality of a cohesive topos
dc.creator.none.fl_str_mv Marmolejo, Francisco
Menni, Matías
author Marmolejo, Francisco
author_facet Marmolejo, Francisco
Menni, Matías
author_role author
author2 Menni, Matías
author2_role author
dc.subject.none.fl_str_mv Topos Theory
Axiomatic Cohesion
topic Topos Theory
Axiomatic Cohesion
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We strengthen a result of Lawvere by proving that every pre-cohesive geometric morphism p: E --> S has a canonical intensive quality s: E --> L. We also discuss examples among bounded pre-cohesive p: E --> S and, in particular, we show that if E is a presheaf topos then so is L.This result lifts to Grothendieck toposes but the sites obtained need not be subcanonical.To illustrate this phenomenon, and also the subtle passage from E to L,we consider a particular family of bounded cohesive toposes over Set and build subcanonical sites fortheir associated categories L.
Fil: Marmolejo, Francisco. Universidad Nacional Autónoma de México; México
Fil: Menni, Matías. Universidad Nacional de La Plata. Facultad de Informática. Laboratorio de Investigación y Formación en Informática Avanzada; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
description We strengthen a result of Lawvere by proving that every pre-cohesive geometric morphism p: E --> S has a canonical intensive quality s: E --> L. We also discuss examples among bounded pre-cohesive p: E --> S and, in particular, we show that if E is a presheaf topos then so is L.This result lifts to Grothendieck toposes but the sites obtained need not be subcanonical.To illustrate this phenomenon, and also the subtle passage from E to L,we consider a particular family of bounded cohesive toposes over Set and build subcanonical sites fortheir associated categories L.
publishDate 2021
dc.date.none.fl_str_mv 2021-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/164666
Marmolejo, Francisco; Menni, Matías; The canonical intensive quality of a cohesive topos; Theory And Applications Of Categories; Theory And Applications Of Categories; 36; 9; 10-2021; 250-279
1201-561X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/164666
identifier_str_mv Marmolejo, Francisco; Menni, Matías; The canonical intensive quality of a cohesive topos; Theory And Applications Of Categories; Theory And Applications Of Categories; 36; 9; 10-2021; 250-279
1201-561X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.tac.mta.ca/tac/volumes/36/9/36-09abs.html
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Theory And Applications Of Categories
publisher.none.fl_str_mv Theory And Applications Of Categories
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.087074

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