Cocomplete toposes whose exact completions are toposes

Título:

Cocomplete toposes whose exact completions are toposes

Autor:

Menni, Matías

Colaboradores:

; 

Temas:

TEORÍA DE CATEGORÍASMATEMÁTICA DE LA COMPUTACIÓN

En:

Journal of Pure and Applied Algebra 210 (2007) 511–520.

Resumen:

Let E be a cocomplete topos. We show that if the exact completion of E is a topos then every indecomposable object in E 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. Copyright 2006 Elsevier B.V.

URL/DOI:

Medio:

Soporte electrónico

Tipo de documento:

Artículo

Idioma:

Inglés

Publicación:

, 2007

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