Globalization of partial inverse semigroupoid actions on sets

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.

arXiv comment19 pages, 1 figure, 3 diagrams and 1 table