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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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2007
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/83213 |
| Aporte de: |
| 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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