Extending the Ehresmann-Schein-Nambooripad Theorem

TL;DR

This paper extends the Ehresmann-Schein-Nambooripad Theorem to include meet-premorphisms for two-sided restriction semigroups and inductive categories, broadening its applicability in the study of partial actions.

Contribution

It introduces an Ehresmann-Schein-Nambooripad-type theorem for meet-premorphisms, complementing previous results for join-premorphisms, and applies it to inverse semigroups.

Findings

Extended the theorem to meet-premorphisms

Established a new correspondence for two-sided restriction semigroups

Derived a corollary for inverse semigroups

Abstract

We extend the `join-premorphisms' part of the Ehresmann-Schein-Nambooripad Theorem to the case of two-sided restriction semigroups and inductive categories, following on from a result of Lawson (1991) for the `morphisms' part. However, it is so-called `meet-premorphisms' which have proved useful in recent years in the study of partial actions. We therefore obtain an Ehresmann-Schein-Nambooripad-type theorem for meet-premorphisms in the case of two-sided restriction semigroups and inductive categories. As a corollary, we obtain such a theorem in the inverse case.