Uniform Algebras

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 the same as they do that of ConA. The category V[CHUnif] of complete, Hausdorff uniform algebras in the variety V is particularly interesting; it has a factorization system 〈E,M〉, and V embeds into V[CHUnif] in such a way that E ∩V is the subcategory of onto and E ∩V the subcategory of one-one homomorphisms.