The locally connected coclosure of a Grothendieck topos Original Research Article

Locally connected Grothendieck toposes are shown to be coreflective in Grothendieck toposes. We refer to this coreflection as locally connected coclosure. The locally connected coclosure of a localic topos is localic. A topos and its locally connected coclosure are seen to have equivalent categories of Lawvere distributions. A class of locales is produced whose locally connected coclosures are trivial. We show how the locally connected coclosure can be described in terms of the locally connected coclosure of a localic cover.