Globalization of partial inverse semigroupoid actions on sets

2023/10/12 by Paulinho Demeneghi, Demeneghi, Paulinho, Felipe Augusto Tasca +1 · 1 citation
Computer Science · Decision Sciences · Mathematics · #18B40 (Primary) #20M30 (Secundary) #Advanced Topics in Algebra #Category Theory (math.CT) #Dynamical Systems (math.DS) #FOS: Mathematics #Fuzzy and Soft Set Theory #Operator Algebras (math.OA) #Rings and Algebras (math.RA) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2310.08693

openalex publication_date 2023/10/12 · openalex created_date 2023/10/17 · openalex updated_date 2026/07/28

Abstract

We prove that every partial action of an inverse semigroupoid on a set admits a universal globalization. Moreover, we show that our construction gives a reflector from the category of partial actions on the full subcategory of global actions. Finally, we investigate if the mediating function given by the universal property of our construction is injective.

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