Congruences of convex algebras

We provide a full description of congruence relations of finitely generated convex, positively convex, and absolutely convex algebras. As a consequence of this result we obtain that finitely generated convex (positively convex, absolutely convex) algebras are finitely presentable. Convex algebras are important in the area of probabilistic systems. In particular positively convex algebras are, as they are the Eilenberg–Moore algebras of the subdistribution monad.