We characterize strongly finitary monads on categories Pos, CPO and DCPO as precisely those preserving sifted colimits. Or, equivalently, enriched finitary monads preserving reflexive coinserters. We study sifted colimits in general enriched categories. For CPO and DCPO we characterize varieties of continuous algebras as precisely the monadic categories for strongly finitary monads.
Keywords: sifted colimit, monad, continuous algebra
2020 MSC: 18C15
Theory and Applications of Categories, Vol. 44, 2025, No. 3, pp 84-131.
Published 2025-01-14.
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