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Ultrasheaves and Double Negation
journal contribution
posted on 2003-04-03, 00:00 authored by Steven AwodeySteven Awodey, Jonas EliassonMoerdijk 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.