A Double Categorical View on Representations of Etendues

Darien DeWolf; Dorette Pronk

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arXiv · 1910.02540

A Double Categorical View on Representations of Etendues

Darien DeWolf·Dorette Pronk

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Abstract

In this paper we introduce a description of ordered groupoids as a particular type of double categories. This enables us to turn Lawson's correspondence between ordered groupoids and left-cancellative categories into a biequivalence. We use this to identify which ordered functors are maps of sites in the sense that they give rise to geometric morphisms between the induced sheaf categories, and establish a Comparison Lemma for maps between Ehresmann sites.

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Darien DeWolf, Dorette Pronk. 2019-10-06. A Double Categorical View on Representations of Etendues. https://arxiv.org/abs/1910.02540

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