Algebras with a compatible uniformity

Abstract

Given a variety of algebras V, we study categories of algebras in V with a compatible structure of uniform space. The lattice of compatible uniformities of an algebra, Unif A, can be considered a generalization of the lattice of congruences Con A. Mal'cev properties of V influence the structure of Unif A, much as they do that of Con A. The category V[CHUnif] of complete, Hausdorff uniform algebras in the variety V is particularly interesting; it has a natural factorization system extending the usual (onto, one-one) factorization system of V.