Algebras of filter-related monads: I. Ultrafilters and Manes’ theorem

In 1969, Ernest Manes proved the following remarkable result: the algebras of the ultrafilter monad on Set are exactly the compact Hausdorff spaces. This is remarkable, because it gives a purely algebraic/category-theoretic of the otherwise purely topological notion of compact Hausdorff spaces. I will explain how this is proved, and I will give a few pointers to some extension results of the same kind. Read the full post.

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