Geodesic
Remarks on punctual local connectedness
Theory and applications of categories, Tome 25 (2011), pp. 51-63 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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We study the condition, on a connected and locally connected geometric morphism $p : \cal E \to \cal S$, that the canonical natural transformation $p_*\to p_!$ should be (pointwise) epimorphic - a condition which F.W. Lawvere called the `Nullstellensatz', but which we prefer to call `punctual local connectedness'. We show that this condition implies that $p_!$ preserves finite products, and that, for bounded morphisms between toposes with natural number objects, it is equivalent to being both local and hyperconnected.

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Classification : Primary 18B25, secondary 18A40
Keywords: axiomatic cohesion, locally conected topos 
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     author = {Peter Johnstone},
     title = {Remarks on punctual local connectedness},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2011_25_a2/}
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Peter Johnstone. Remarks on punctual local connectedness. Theory and applications of categories, Tome 25 (2011), pp. 51-63. http://geodesic.mathdoc.fr/item/TAC_2011_25_a2/