Continuous cohesion over sets

Autores
Menni, Matías
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A pre-cohesive geometric morphism p : E → S satisfies Continuity if the canonical p!(Xp ∗S) → (p!X) S is an iso for every X in E and S in S. We show that if S = Set and E is a presheaf topos then, p satisfies Continuity if and only if it is a quality type. Our proof of this characterization rests on a related result showing that Continuity and Sufficient Cohesion are incompatible for presheaf toposes. This incompatibility raises the question whether Continuity and Sufficient Cohesion are ever compatible for Grothendieck toposes. We show that the answer is positive by building some examples.
Fil: Menni, Matías. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Materia
Axiomatic Cohesion
Topos
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:11336/46008
Acceder
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spelling Continuous cohesion over setsMenni, MatíasAxiomatic CohesionToposhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A pre-cohesive geometric morphism p : E → S satisfies Continuity if the canonical p!(Xp ∗S) → (p!X) S is an iso for every X in E and S in S. We show that if S = Set and E is a presheaf topos then, p satisfies Continuity if and only if it is a quality type. Our proof of this characterization rests on a related result showing that Continuity and Sufficient Cohesion are incompatible for presheaf toposes. This incompatibility raises the question whether Continuity and Sufficient Cohesion are ever compatible for Grothendieck toposes. We show that the answer is positive by building some examples.Fil: Menni, Matías. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaMount Allison University2014-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/46008Menni, Matías; Continuous cohesion over sets; Mount Allison University; Theory And Applications Of Categories; 29; 20; 11-2014; 542-5681201-561XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.tac.mta.ca/tac/volumes/29/20/29-20.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:03:29Zoai:ri.conicet.gov.ar:11336/46008instacron: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:34982025-09-03 10:03:29.749CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Continuous cohesion over sets
title Continuous cohesion over sets
spellingShingle Continuous cohesion over sets
Menni, Matías
Axiomatic Cohesion
Topos
title_short Continuous cohesion over sets
title_full Continuous cohesion over sets
title_fullStr Continuous cohesion over sets
title_full_unstemmed Continuous cohesion over sets
title_sort Continuous cohesion over sets
dc.creator.none.fl_str_mv Menni, Matías
author Menni, Matías
author_facet Menni, Matías
author_role author
dc.subject.none.fl_str_mv Axiomatic Cohesion
Topos
topic Axiomatic Cohesion
Topos
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv A pre-cohesive geometric morphism p : E → S satisfies Continuity if the canonical p!(Xp ∗S) → (p!X) S is an iso for every X in E and S in S. We show that if S = Set and E is a presheaf topos then, p satisfies Continuity if and only if it is a quality type. Our proof of this characterization rests on a related result showing that Continuity and Sufficient Cohesion are incompatible for presheaf toposes. This incompatibility raises the question whether Continuity and Sufficient Cohesion are ever compatible for Grothendieck toposes. We show that the answer is positive by building some examples.
Fil: Menni, Matías. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
description A pre-cohesive geometric morphism p : E → S satisfies Continuity if the canonical p!(Xp ∗S) → (p!X) S is an iso for every X in E and S in S. We show that if S = Set and E is a presheaf topos then, p satisfies Continuity if and only if it is a quality type. Our proof of this characterization rests on a related result showing that Continuity and Sufficient Cohesion are incompatible for presheaf toposes. This incompatibility raises the question whether Continuity and Sufficient Cohesion are ever compatible for Grothendieck toposes. We show that the answer is positive by building some examples.
publishDate 2014
dc.date.none.fl_str_mv 2014-11
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/11336/46008
Menni, Matías; Continuous cohesion over sets; Mount Allison University; Theory And Applications Of Categories; 29; 20; 11-2014; 542-568
1201-561X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/46008
identifier_str_mv Menni, Matías; Continuous cohesion over sets; Mount Allison University; Theory And Applications Of Categories; 29; 20; 11-2014; 542-568
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/29/20/29-20.pdf
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 Mount Allison University
publisher.none.fl_str_mv Mount Allison University
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 13.13397

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