Partial Semigroupoid Actions on Sets

TL;DR

This paper introduces a unified framework for partial actions of semigroupoids on sets, extending existing theories for categories and semigroups with a universal globalization construction.

Contribution

It generalizes the concept of partial actions to semigroupoids and provides a universal globalization method that unifies previous approaches for categories and semigroups.

Findings

Universal globalization exists for partial semigroupoid actions

Extends partial category action theory by Nystedt and Lundström

Unifies partial actions theories for categories and semigroups

Abstract

We introduce partial semigroupoid actions on sets and demonstrate that each such action admits universal globalization. Our construction extends the universal globalization for partial category actions given by P. Nystedt (Lundstr\"om) and the tensor product globalization for strong partial semigroup actions given by G. Kudryavtseva and V. Laan, thereby unifying the theory of partial actions for both categories and semigroups.