- - Date: Wed, 01 Feb 1995 11:51:57 +0000 - 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 - - Andrea Schalk - University of Cambridge - Computer Lab - - Andrea.Schalk@cl.cam.ac.uk - - I don't know of an explicit reference, but things of this sort are certainly familiar. Look, for example, at the proof in TTT that toposes are cartesian closed. For that matter, the proof that a slice of a topos is a topos uses the same idea. Michael Barr