  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groupoids is used to give a proof for the (known, but apparently unpublished)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.
