Oberseminar WS2025/26

It is well known that all c-basic varieties, studied by Mardare, Panangaden and Plotkin, are monadic categories over Met, the category of extended metric spaces. This opens the question of which monads correspond to those varieties.

For c=ω, all enriched finitary monads have that property. But Urbat presented an example of an ω-basic variety yielding a non-finitary monad.

We prove that a monad corresponds to an ω-basic variety iff it is a weighted colimit of finitary monads (in the category Mnd(Met) of enriched monads). Further, a monad corresponds to a c-basic variety for an uncountable cardinal c iff it is enriched and c-accessible.