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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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2007 |
| País: | Argentina |
| Institución: | Universidad Nacional de La Plata |
| Repositorio: | SEDICI (UNLP) |
| Idioma: | inglés |
| OAI Identifier: | oai:sedici.unlp.edu.ar:10915/83213 |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/83213 |
| Access Level: | acceso abierto |
| Palabra clave: | Ciencias Informáticas cocomplete topos Grothendieck toposes |
| Sumario: | 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. |
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