  In this article, we introduce the concept of partial groupoid actions on R-
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 R-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.
