A Double Categorical View on Representations of Etendues
Category Theory
2019-10-08 v1
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.
Keywords
Cite
@article{arxiv.1910.02540,
title = {A Double Categorical View on Representations of Etendues},
author = {Darien DeWolf and Dorette Pronk},
journal= {arXiv preprint arXiv:1910.02540},
year = {2019}
}
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35 pages