Ultrasheaves and Double-Negation
journal contributionposted on 13.11.2002, 00:00 by Steve Awodey, Jonas Eliasson
Moerdijk has introduced a topos of sheaves on a category of filters. Following his suggestion, we prove that its double negation subtopos is the topos of sheaves on the subcategory of ultrafilters - the ultrasheaves. We then use this result to establish a double negation translation of results between the topos of ultrasheaves and the topos on filters.