Left cancellative semigroups

A left cancellative semigroup is a semigroup S = (S,·) such that · is left cancellative: z·x = z·y ⇒ x = y.

Let S and T be left cancellative semigroups. A morphism from S to T is a function h : S→T that is a homomorphism: h(xy) = h(x)h(y).

(N, + ), the natural numbers, with additition.

Classtype	Quasivariety
Equational theory
Quasiequational theory
First-order theory
Locally finite	No
Residual size
Congruence distributive	No
Congruence modular	No
Congruence n-permutable	No
Congruence regular	No
Congruence uniform	No
Congruence extension property
Definable principal congruences
Equationally definable principal congruences	No
Amalgamation property	No
Strong amalgamation property	No
Epimorphisms are surjective	No

[Size 1]?: 1
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[Left cancellative monoids]?
Cancellative semigroups