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A groupoid is a category where all morphisms are invertible. This notion can also be seen as an extension of the notion of group. A motivating example is the fundamental groupoid of a topological space with respect to several base points, compared to the usual fundamental group.

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Group actions on principal groupoids

Suppose that $\mathcal{G}$ is etale principal groupoid and that $G$ is a discrete (or finite) group acting freely on the locally compact unit space $\mathcal{G}^0$ (or assuming compactness, if necessa …