A pointed variety V is Jonsson-Tarski if its theory has a unique constant 0 and contains a binary operation + such that 0+x = x = x+0. It will be shown that a pointed variety V is Jonsson-Tarski if and only if, given any pair (X,Y) of algebras, and considering the diagram:

X --> X x Y <-- Y

the (sub)algebra X x Y is the supremum of the "subalgebras" X and Y. Thus, a classical Universal Algebra presentation is equivalent to a categorical presentation. The main aim of this talk is to compare or confront the different ways of defining commutativity in these equivalent contexts.