papers on colimits of monads available

[Jiri Adamek <adamek@iti.cs.tu-bs.de>]

I would like to announce two papers available on arxiv:

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J. Adamek, N. Bowler, P. Levy and S. Milius:
Coproducts of Monads on Set (http://arxiv.org/abs/1409.3804)

(This is an abstract, extended by proofs in the appendix, of a talk
presented at LICS 2012.)

A monad M on Set is proved to have a coproduct with every monad in
the category Monad(Set) iff M is a submonad of either the terminal
monad (constant to 1) or an exception monad (sending X to X+E). Calling
such monads trivial, we prove that a coproduct of nontrivial monads
exists iff the monads have arbitrarily large joint pre-fixpoints.
(A pre-fixpoint of an endofunctor M is an object X such that MX is
a subobject of X.) A surprisingly simple formula for coproducts of monads
in Set is presented

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J. Adamek: Colimits of Monads (http://arxiv.org/abs/1409.3805)

For "set-like" categories A the category Monad(A) is proved to
have coequalizers. It also has a colimit of every diagram
such that arbitrarily large joint pre-fixpoints of all the monads
exist. This is stronger than the well-known fact that accessible
monads admit all colimits. Somewhat surprisingly, the category of monads
on Gra does not have coequalizers.



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