Partial groupoid actions on R-categories: Globalization and the smash product

Abstract

In this paper, we introduce the concept of partial groupoid actions on [Formula: see text]-semicategories as well as we give criteria for existence of a globalization of it. This point of view is a generalization of the notions of partial groupoid actions on rings and partial group action on an [Formula: see text]-semicategory. We also define the notions of partial skew groupoid category, smash product and describe functorial relations between them, in particular we show that the smash product is a Galois covering of its associated skew groupoid category.