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.
Dialectica principles via G¨ odel doctrines.Theoretical Computer Science, 947:Paper No
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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.