  For a set of sorts $S$ and an $S$-sorted signature $\Sigma$ we prove that a
profinite $\Sigma$-algebra, i.e., a projective limit of a projective system of
finite $\Sigma$-algebras, is a retract of an ultraproduct of finite
$\Sigma$-algebras if the family consisting of the finite $\Sigma$-algebras
underlying the projective system is with constant support. In addition, we
provide a categorial rendering of the above result. Specifically, after
obtaining a category where the objects are the pairs formed by a nonempty
upward directed preordered set and by an ultrafilter containing the filter of
the final sections of it, we show that there exists a functor from the just
mentioned category whose object mapping assigns to an object a natural
transformation which is a retraction.
