Abstract
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.
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