Abstract
In this paper necessary and sufficient conditions are given on a concrete category over a category
B so that it can be densely embedded (over
B) into a geometric topological category
E that admits certain universal final lifts. These conditions, as well as the class of universal final lifts, depend upon an a priori given full subcategory Δ of
B. For example,
E may have, depending upon Δ and
B, universal coproducts or quotients or colimits. For appropriate Δ's, if
B is cartesian closed then so is
E.
