  Profinite equations are an indispensable tool for the algebraic
classification of formal languages. Reiterman's theorem states that they
precisely specify pseudovarieties, i.e.~classes of finite algebras closed under
finite products, subalgebras and quotients. In this paper, Reiterman's theorem
is generalized to finite Eilenberg-Moore algebras for a monad T on a category
D: we prove that a class of finite T-algebras is a pseudovariety iff it is
presentable by profinite equations. As a key technical tool, we introduce the
concept of a profinite monad associated to the monad T, which gives a
categorical view of the construction of the space of profinite terms.
