Partial Semigroupoid Actions on Sets
Rafael Haag Petasny, Tha\'isa Tamusiunas

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.
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Taxonomy
TopicsFunctional Equations Stability Results · Fuzzy and Soft Set Theory · Advanced Topics in Algebra
