  A coextensive category can be defined as a category $\mathcal{C}$ with finite
products such that for each pair $X,Y$ of objects in $\mathcal{C}$, the
canonical functor $\times\colon X/\mathcal{C} \times Y/\mathcal{C} \to (X
\times Y)/\mathcal{C}$ is an equivalence. We give a syntactical
characterization of coextensive varieties of universal algebras. This paper is
an updated version of the pre-print arXiv:2008.03474
