Exponentiation in V-categories
Abstract: For a Heyting algebra V which, as a category, is
monoidal closed, we obtain characterizations of exponentiable objects and
morphisms in the category of V-categories and apply them to some well-known
examples. In the case V=[0,infty] these characterizations
of exponentiable morphisms and objects in the categories PMet of (pre)metric
spaces and non-expansive maps show in particular that exponentiable metric
spaces are exactly the almost convex metric spaces, while exponentiable
complete metric spaces are the complete totally convex ones.
