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Colimits of Monads

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If you have a question about this talk, please contact Nathan Bowler.

Colimits in the category of monads on a given category C are studied. For example coequalizers always exist, assuming C is complete and wellpowered.

For monads on Set a coproduct exists whenever the monads have arbitrarily large common fixed points. This condition is also necessary in case of free monads. Two free monads are presented whose coproduct does not exist.

The result of N. Ghani and T. Uustalu that coproducts of ideal monads are ideal is generalized to all colimits of ideal monads.

This is joint work with P.B. Levy and S. Milius.

This talk is part of the Category Theory Seminar series.

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