Cocomplete toposes whose exact completions are toposes

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 charact...

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Autor principal: Menni, Matías
Formato: Articulo
Lenguaje:Inglés
Publicado: 2007
Materias:
Ciencias Informáticas
cocomplete topos
Grothendieck toposes
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/83213
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-83213
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Ciencias Informáticas
cocomplete topos
Grothendieck toposes
spellingShingle Ciencias Informáticas
cocomplete topos
Grothendieck toposes
Menni, Matías
Cocomplete toposes whose exact completions are toposes
topic_facet Ciencias Informáticas
cocomplete topos
Grothendieck toposes
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.
format Articulo
Articulo
author Menni, Matías
author_facet Menni, Matías
author_sort Menni, Matías
title Cocomplete toposes whose exact completions are 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
publishDate 2007
url http://sedici.unlp.edu.ar/handle/10915/83213
work_keys_str_mv AT mennimatias cocompletetoposeswhoseexactcompletionsaretoposes
bdutipo_str Repositorios
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