On the uniformization of lattice-valued frames

In this note we discuss the appropriate way of uniformizing the notion of a lattice-valued frame introduced by Pultr and Rodabaugh in 2003. We cover the case of a completely distributive lattice (which is, in a certain sense, the most general one) and study the corresponding category of uniform lattice-valued frames. In particular, we show that this is a complete and cocomplete category that extends in a nice manner the category of uniform frames, widely studied in the literature.