On Ehresmann semigroups

Abstract

We describe an alternative approach to describing Ehresmann semigroups by categories in which a class of étale actions plays an important rôle. We also characterize the Ehresmann semigroups that arise as the set of all subsets of a finite category. As an application, we prove that every birestriction semigroup can be suitably embedded into a birestriction semigroup constructed from a category. As a corollary, we determine when a birestriction semigroup can be suitably embedded into an inverse semigroup.