Galois correspondence for group-type partial actions of groupoids

Abstract

Let $G$ be a finite groupoid and $\alpha=(S_g,\alpha_g)_{g\in G}$ a unital partial action of group-type of $G$ on a commutative ring $S=\oplus_{y\in G_0}S_y$. We 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.