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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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vote
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. …
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vote
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 …