Toposes of connectivity spaces. Morita equivalences with topological spaces and partially ordered sets in the finite case

Stéphane Dugowson

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arXiv · 1803.02275

Toposes of connectivity spaces. Morita equivalences with topological spaces and partially ordered sets in the finite case

Stéphane Dugowson

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Abstract

This paper has two parts. First, we recall and detail the definition of the Grothendieck topos of a connectivity space, that is the topos of sheaves on such a space. In the second part, we prove that every finite connectivity space is Morita-equivalent to a finite topological space, and vice versa (we have given this proof in several, but we haven't yet shared this in writing).

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Stéphane Dugowson. 2018-03-06. Toposes of connectivity spaces. Morita equivalences with topological spaces and partially ordered sets in the finite case. https://arxiv.org/abs/1803.02275

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