  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 generalised to finite Eilenberg-Moore algebras for a monad T on a variety D
of (ordered) algebras: a class of finite T-algebras is a pseudovariety iff it
is presentable by profinite (in-)equations. As an application, quasivarieties
of finite algebras are shown to be presentable by profinite implications. Other
examples include finite ordered algebras, finite categories, finite
infinity-monoids, etc.
