Mathematics – Category Theory
Scientific paper
2011-11-12
Mathematics
Category Theory
Long note version. 36 pages
Scientific paper
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for equivariant sheaf toposes on open topological groupoids is used to give a proof for the (known, but apparently unpublished) proposition that if H is a strictly full subgroupoid of an open topological groupoid G, then the topos of equivariant sheaves on H is a subtopos of the topos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. A self-contained presentation of Moerdijk's site description is included for the case of open topological, rather than localic, groupoids. In the final section, the site description is used to give an intrinsic characterization of those open topological groupoids that induce toposes which have a generating set of compact objects and the property that a finite product of compact objects is compact. This generalizes a known characterization of coherent topological groups.
Forssell Henrik
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