Galois correspondence for group-type partial actions of groupoids

Abstract

Let G be a finite groupoid and α = (Sg, αg)g∈G a unital partial action of group-type of G on a commutative ring S = ⊕y∈G0Sy. We shall prove a Galois correspondence between a class of wide subgroupoids of G and a class of subrings of S. We recover known results for global groupoid actions and we give several examples to illustrate the correspondence.