A Heyting algebra is a structure A = (A,∨,0,∧,1,→) such that
(A,∨,0,∧,1) is a bounded distributive lattice, and
→ gives the residual of ∧: x∧y ≤ z ⇔ y ≤ x→z.
A Heyting algebra is a FLew-algebra A = (A,∨,0,∧,1,·,→) such that
x∧y = x·y.
Let A and B be Heyting algebras. A morphism from A to B is a function h : A→B that is a homomorphism: h(x∨y) = h(x)∨h(y) and h(0) = 0 and h(x∧y) = h(x)∧h(y) and h(1) = 1 and h(x→y) = h(x)→h(y).
|Congruence n-permutable||yes, n = 2|
|Congruence e-regular||yes, e = 1|
|Congruence extension property||yes|
|Definable principal congruences||yes|
|Equationally definable principal congruences||yes|
|Strong amalgamation property||yes|
|Epimorphisms are surjective||yes|