This note discusses the appropriate way of uniformizing the notion
of an L-valued frame introduced by A. Pultr and S. Rodabaugh in [Lattice-valued
frames, functor categories, and classes of sober spaces, Chapter 6 of Topological
and Algebraic Structures in Fuzzy Sets: A Handbook of Recent Developments in
the Mathematics of Fuzzy Sets, Kluwer, 2003]. It covers the case of a completely
distributive lattice L (which is, in a certain sense, the most general one) and studies
the corresponding category of uniform L-valued frames