re Algebraic structures for Eilenberg-Moore algebras

''From: Andrea Schalk <Andrea.Schalk@cl.cam.ac.uk> I'm looking for some pointer to literature where I can find the following (or a similar) Theorem: Let $(T,\eta,\mu)$ be a monad. Assume we have an algebraic structure such that every free algebra for that monad carries one of those algebraic structures and such that all morphisms of the form $Tf$ and all $\mu_C$ preserve it. Then all Eilenberg-Moore algebras carry such a structure and all morphisms between them preserve it. Thanks'' I don't know where to look for such a theorem but would be more optimistic if I knew what 'carries' means. Harvey Friedman published something of this tendency about 1977, I think with semantic hypothesis and syntactic conclusion. John Isbell