High Quality Content by WIKIPEDIA articles!A congruence ? of a join-semilattice S is monomial, if the ?-equivalence class of any element of S has a largest element. We say that ? is distributive, if it is a join, in the congruence lattice Con S of S, of monomial join-congruences of S. The following definition originates in Schmidt's 1968 work and was subsequently adjusted by Wehrung. Definition (weakly distributive homomorphisms). A homomorphism ? : S ? T between join-semilattices S and T is weakly distributive, if for all a, b in S and all c in T such that ?(c)? a ? b, there are elements x and y of S such that c? x ? y, ?(x)? a, and ?(y)? b.

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