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Motivation: Let $(X,\tau)$ be a topological space. Then the set $\beta X$ of ultrafilters on $X$ admits a natural topology (cf. Example 5.14 in Adámek and Sousa - D-ultrafilters and their monads), ...

Compact Hausdorff spaces are algebras of the ultrafilter monad on Set. Is the category of Tychonoff spaces also monadic over Set?

(I'm going to try to use definitions from Abstract and Concrete Categories: The Joy of Cats by Adámek, Herrlich, and Strecker, since both of the adjectives in the title of my question seem to have at ...

Let $\mathsf{Stone}$ denote the category of Stone spaces (compact, totally disconnected Hausdorff spaces) and continuous maps. The forgetful functor $U : \mathsf{Stone} \to \mathsf{Set}$ has a left ...