preprint announcement - related to Todd Wilson's question

preprint announcement - related to Todd Wilson's question

[Panagis Karazeris]

Dear categorists,

I would like to announce that the following preprint is available from my
webpage

www.math.upatras.gr/~pkarazer

P. Karazeris and J. Velebil, Dense morphisms of monads.

Abstract:
Given an arbitrary locally finitely presentable category K and finitary
monads T and S on K,
we characterize monad morphisms \alpha : S --> T with the property that
the induced functor \alpha _* : K^T --> K^S
between the categories of Eilenberg-Moore algebras is fully faithful.
We call such monad morphisms dense and give a characterization of them in
the spirit of Beth’s definability theorem: \alpha is a dense monad
morphism
if and only if every T-operation is explicitly defined using S-operations.
We also give a characterization in terms of epimorphic property of \alpha
and clarify the connection between various notions of epimorphisms
between monads.

The above work bears some relation to the question posed by Todd Wilson on
implicitly definable operations. The connection though with non-surjective
epimorphisms is not pursued here.

Best regards,
Panagis Karazeris