A complemented lattice is a bounded lattice L = (L,∨,0,∧,1) such that every element has a complement: ∃y(x∨y = 1 and x∧y = 0).
Let L and M be complemented lattices. A morphism from L to M is a function h : L→M that is a bounded lattice homomorphism: h(x∨y) = h(x)∨h(y) and h(x∧y) = h(x)∧h(y) and h(0) = 0 and h(1) = 1.
(P(S),∪,Ø,∩,S), the collection of subsets of a set S, with union, empty set, intersection, and the whole set S.
|Congruence extension property||no|
|Definable principal congruences||no|
|Equationally definable principal congruences||no|
|Strong amalgamation property|
|Epimorphisms are surjective|