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 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.

22 pages