Ultrasheaves and Double Negation

2003-04-03T00:00:00Z (GMT) by Steven 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.