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About: Distributive homomorphism     Goto   Sponge   NotDistinct   Permalink

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A congruence θ of a join-semilattice S is monomial, if the θ-equivalence class of any element of S has a largest element. We say that θ 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. Examples: (2) For a convex sublattice K of a lattice L, the canonical (∨, 0)-homomorphism from Conc K to Conc L is weakly distributive.