An Ehresmann-Schein-Nambooripad-type theorem for left restriction semigroupoids

TL;DR

This paper generalizes the Ehresmann-Schein-Nambooripad theorem to left restriction semigroupoids by introducing locally inductive constellations, establishing new categorical isomorphisms and extending existing results.

Contribution

It introduces locally inductive constellations and proves an ESN-type theorem for left restriction semigroupoids, broadening the theoretical framework.

Findings

Establishes isomorphisms between left restriction semigroupoids and locally inductive constellations

Generalizes ESN theorem to new algebraic structures

Provides ESN-type theorems for restriction categories and inverse semigroupoids

Abstract

We introduce the concept of locally inductive constellations and establish isomorphisms between the categories of left restriction semigroupoids and locally inductive constellations. This construction offers an alternative to the celebrated Ehresmann-Schein-Nambooripad (ESN) Theorem and, in particular, generalizes results for one-sided restriction semigroups. We also obtain ESN-type theorems for one-sided restriction categories and inverse semigroupoids.