The authors construct a tripos and topos for extended Weihrauch degrees and show the Kleene-Vesley topos arises as j-sheaves for a Lawvere-Tierney topology on it.
The degree structure of Weihrauch- reducibility.Logical Methods in Computer Science, Volume 9, Issue 2, 2013
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A topos for extended Weihrauch degrees
The authors construct a tripos and topos for extended Weihrauch degrees and show the Kleene-Vesley topos arises as j-sheaves for a Lawvere-Tierney topology on it.