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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
participants (1)
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Jiri Adamek