Sifted Colimits, Strongly Finitary Monads and Continuous Algebras

We characterize strongly finitary monads on categories $\mathsf{P}\mathsf{o}\mathsf{s}$, $\mathsf{C}\mathsf{P}\mathsf{O}$ and $\mathsf{D}\mathsf{C}\mathsf{P}\mathsf{O}$ as precisely those preserving sifted colimits. Or, equivalently, enriched finitary monads preserving reflexive coinserters. We study sifted colimits in general enriched categories. For $\mathsf{C}\mathsf{P}\mathsf{O}$ and $\mathsf{D}\mathsf{C}\mathsf{P}\mathsf{O}$ we characterize varieties of continuous algebras as precisely the monadic categories for strongly finitary monads.