# Commit 2020-10-12 23:17 d1bb5ea6

View on Github →feat(topology/category/Compactum): Compact Hausdorff spaces (#4555) This PR provides the equivalence between the category of compact Hausdorff topological spaces and the category of algebras for the ultrafilter monad.

## Notation

`Compactum`

is the category of algebras for the ultrafilter monad. It's a wrapper around`monad.algebra (of_type_functor $ ultrafilter)`

.`CompHaus`

is the full subcategory of`Top`

consisting of topological spaces which are compact and Hausdorff.