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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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Accepted
Groupoids and hypergroups
Yes, the notion of hypergroupoids exits. See the following preprints:
http://arxiv.org/abs/1403.3424
http://arxiv.org/abs/1402.0072
Both the articles are published. The second article defines Haar …
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Groupoid actions on spaces
Meyer, Buss and Zhu show that, in discrete cases, these actions are same as equivalent to saturated Fell bundles on groupoids. This result is true when $G$ is a topological group. …