  We discuss conditions under which certain compactifications of topological
spaces can be obtained by composing the ultrafilter space monad with suitable
reflectors. In particular, we show that these compactifications inherit their
categorical properties from the ultrafilter space monad. We further observe
that various constructions such as the prime open filter monad defined by H.
Simmons, the prime closed filter compactification studied by Bentley and
Herrlich, as well as the separated completion monad studied by Salbany fall
within the same categorical framework.
