A categorical generalization of the notion of movability from inverse systems and shape theory was given by the first author who defined the notion of movable category and used it to interpret the movability of topological spaces. In this paper the authors define the notion of uniformly movable category and prove that a topological space is uniformly movable in the sense of shape theory if and only if its comma category in the homotopy category HTop over the subcategory HPol of polyhedra is uniformly...