#
Dense morphisms of monads

##
Panagis Karazeris, Jiri Velebil

Given an arbitrary locally finitely presentable category $K$
and finitary monads $T$ and $S$ on $K$, we characterize
monad morphisms $\alpha: S\to T$ with the property
that the induced functor $\alpha_*: K^T \to K^ S$ 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.

Keywords:
Definable operation, monad morphism, locally finitely
presentable category

2000 MSC:
18C20, 18C35

*Theory and Applications of Categories,*
Vol. 18, 2007,
No. 14, pp 372-399.

http://www.tac.mta.ca/tac/volumes/18/14/18-14.dvi

http://www.tac.mta.ca/tac/volumes/18/14/18-14.ps

http://www.tac.mta.ca/tac/volumes/18/14/18-14.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/18/14/18-14.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/18/14/18-14.ps

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