Cocomplete toposes whose exact completions are toposes

Autores
Menni, Matías
Año de publicación
2007
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let ε be a cocomplete topos. We show that if the exact completion of ε is a topos then every indecomposable object in ε is an atom. As a corollary we characterize the locally connected Grothendieck toposes whose exact completions are toposes. This result strengthens both the Lawvere-Schanuel characterization of Boolean presheaf toposes and Hofstra's characterization of the locally connected Grothendieck toposes whose exact completion is a Grothendieck topos. We also show that for any topological space X, the exact completion of Sh (X) is a topos if and only if X is discrete. The corollary in this case characterizes the Grothendieck toposes with enough points whose exact completions are toposes.
Laboratorio de Investigación y Formación en Informática Avanzada
Materia
Ciencias Informáticas
cocomplete topos
Grothendieck toposes
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/83213
Acceder
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spelling Cocomplete toposes whose exact completions are toposesMenni, MatíasCiencias Informáticascocomplete toposGrothendieck toposesLet ε be a cocomplete topos. We show that if the exact completion of ε is a topos then every indecomposable object in ε is an atom. As a corollary we characterize the locally connected Grothendieck toposes whose exact completions are toposes. This result strengthens both the Lawvere-Schanuel characterization of Boolean presheaf toposes and Hofstra's characterization of the locally connected Grothendieck toposes whose exact completion is a Grothendieck topos. We also show that for any topological space X, the exact completion of Sh (X) is a topos if and only if X is discrete. The corollary in this case characterizes the Grothendieck toposes with enough points whose exact completions are toposes.Laboratorio de Investigación y Formación en Informática Avanzada2007info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf511-520http://sedici.unlp.edu.ar/handle/10915/83213enginfo:eu-repo/semantics/altIdentifier/issn/0022-4049info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jpaa.2006.10.009info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-11-05T12:55:06Zoai:sedici.unlp.edu.ar:10915/83213Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-11-05 12:55:06.953SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Cocomplete toposes whose exact completions are toposes
title Cocomplete toposes whose exact completions are toposes
spellingShingle Cocomplete toposes whose exact completions are toposes
Menni, Matías
Ciencias Informáticas
cocomplete topos
Grothendieck toposes
title_short Cocomplete toposes whose exact completions are toposes
title_full Cocomplete toposes whose exact completions are toposes
title_fullStr Cocomplete toposes whose exact completions are toposes
title_full_unstemmed Cocomplete toposes whose exact completions are toposes
title_sort Cocomplete toposes whose exact completions are toposes
dc.creator.none.fl_str_mv Menni, Matías
author Menni, Matías
author_facet Menni, Matías
author_role author
dc.subject.none.fl_str_mv Ciencias Informáticas
cocomplete topos
Grothendieck toposes
topic Ciencias Informáticas
cocomplete topos
Grothendieck toposes
dc.description.none.fl_txt_mv Let ε be a cocomplete topos. We show that if the exact completion of ε is a topos then every indecomposable object in ε is an atom. As a corollary we characterize the locally connected Grothendieck toposes whose exact completions are toposes. This result strengthens both the Lawvere-Schanuel characterization of Boolean presheaf toposes and Hofstra's characterization of the locally connected Grothendieck toposes whose exact completion is a Grothendieck topos. We also show that for any topological space X, the exact completion of Sh (X) is a topos if and only if X is discrete. The corollary in this case characterizes the Grothendieck toposes with enough points whose exact completions are toposes.
Laboratorio de Investigación y Formación en Informática Avanzada
description Let ε be a cocomplete topos. We show that if the exact completion of ε is a topos then every indecomposable object in ε is an atom. As a corollary we characterize the locally connected Grothendieck toposes whose exact completions are toposes. This result strengthens both the Lawvere-Schanuel characterization of Boolean presheaf toposes and Hofstra's characterization of the locally connected Grothendieck toposes whose exact completion is a Grothendieck topos. We also show that for any topological space X, the exact completion of Sh (X) is a topos if and only if X is discrete. The corollary in this case characterizes the Grothendieck toposes with enough points whose exact completions are toposes.
publishDate 2007
dc.date.none.fl_str_mv 2007
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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://sedici.unlp.edu.ar/handle/10915/83213
url http://sedici.unlp.edu.ar/handle/10915/83213
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0022-4049
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jpaa.2006.10.009
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
511-520
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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