Subgroupoids and Quotient Theories
Abstract
Moerdijk's site description for equivariant sheaf toposes on open topological groupoids is used to give a proof for the (known, but apparently unpublished) proposition that if H is a strictly full subgroupoid of an open topological groupoid G, then the topos of equivariant sheaves on H is a subtopos of the topos of equivariant sheaves on G. This proposition is then applied to the study of quotient geometric theories and subtoposes. In particular, an intrinsic characterization is given of those subgroupoids that are definable by quotient theories.
Cite
@article{arxiv.1111.2952,
title = {Subgroupoids and Quotient Theories},
author = {Henrik Forssell},
journal= {arXiv preprint arXiv:1111.2952},
year = {2013}
}
Comments
v1: Long note version, including a self-contained presentation of Moerdijk's site construction for sheaves on open topological groupoids, and an application of this construction to the characterization of coherent groupoids. 36 pages. v2: Short and revised version, accepted for publication. 14 pages