  We formulate an alternative approach to describing Ehresmann semigroups by
means of left and right \'etale actions of a meet semilattice on a category. We
also characterize the Ehresmann semigroups that arise as the set of all subsets
of a finite category. As applications, we prove that every restriction
semigroup can be nicely embedded into a restriction semigroup constructed from
a category, and we describe when a restriction semigroup can be nicely embedded
into an inverse semigroup.
