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1. • CommentRowNumber1.
   • CommentAuthorHarry Gindi
   • CommentTimeNov 15th 2011
   • PermaLink
   Author: Harry Gindi
   Format: MarkdownItexLet $C\to D$ be a functor between small categories, and consider the induced geometric morphism between presheaf categories. Is there a nontrivial condition on the map $C\to D$ such that the internal function object comparison map for the direct image, $f_\ast(A^B)\to f_\ast(A)^{f_\ast(B)}$ is a trivial fibration (weakly orthogonal to the class of monomorphisms)? How about for the inverse image comparison map?

   Let be a functor between small categories, and consider the induced geometric morphism between presheaf categories. Is there a nontrivial condition on the map such that the internal function object comparison map for the direct image, is a trivial fibration (weakly orthogonal to the class of monomorphisms)? How about for the inverse image comparison map?