nLab multimonad




A multimonad is to a multiadjunction what a monad is to an adjunction.

(Note that this is not related to monads on multicategories.)



A multimonad on a category CC comprises a presheaf on CC together with a monad on its category of elements.

Multimonadic categories

Multi-monadic categories on SetSet can be characterized in the following way: they are regular, with connected limits, with coequalizers of coequalizable pairs, their equivalence relations are effective, their forgetful functors preserve coequalizers of equivalence relations and reflect isomorphisms. Unlike monadic categories they need not have products. Examples include local rings, fields, inner spaces, locally compact spaces, locally compact groups, and complete ordered sets. (Diers 80, p.153)

The forgetful functor from a multimonadic category creates connected limits.


  • Yves Diers, Multimonads and multimonadic categories, Journal of Pure and Applied Algebra 17 (1980) 153-170 (pdf)

Last revised on March 16, 2023 at 15:50:47. See the history of this page for a list of all contributions to it.