Coproducts of monads

This is to announce an extended abstract of our paper
  	Coproducts of Monads in Set
that will be presented at the conference LICS 2012.

In the category of monads on Set we give a necessary and
sufficient condition for a coproduct to exist, and a concrete formula
for the coproduct. If one of the monads is inconsistent, i.e. a submonad
of the (trivial) terminal monad, the coproduct is inconsistent.
Another case where the coproduct always exists is the exception monad
SX = X+E: the coproduct with another monad T is given by T(X+E).

Theorem. Two consistent monads on Set have a coproduct iff
they have arbitrarily large joint fixed points, or one is a submonad of the
exception monad. The coproduct injections are monomorphisms.

Example. A monad S has a coproduct with the power-set monad iff
it has coproducts with all monads. This is the case precisely when S i a
submonad of the exception monad, or is inconsistent.

The extended abstract can be downloaded at
  	http://www.iti.cs.tu-bs.de/~milius/publications/papers.html

J. Adamek, N. Bowler, P. Levy and S. Milius

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