We use the theory of triposes to prove that every (non-degenerate) locale H is the set of truth values of a complete and co-complete quasi-topos into which the category of topological spaces embeds and the topos of sheaves over H reflectively embeds.
On a generalization of equilogical spaces / F. Pasquali. - In: LOGICA UNIVERSALIS. - ISSN 1661-8297. - 12:1-2(2018 May), pp. 129-140. [10.1007/s11787-018-0192-9]
On a generalization of equilogical spaces
F. Pasquali
2018
Abstract
We use the theory of triposes to prove that every (non-degenerate) locale H is the set of truth values of a complete and co-complete quasi-topos into which the category of topological spaces embeds and the topos of sheaves over H reflectively embeds.
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