We give a set of axioms for the notion of locally compact hypergroupoids, as an extension of both groupoids and hypergroups, and study their basic properties. We show that, adding a natural condition on the continuity of support, one of the axioms assumed by Renault on the left Haar system automatically follows. We show that an irreducible representation of a compact hypergroupoid is fiberwise finite dimensional.

中文翻译：

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局部紧缩超群体

我们给出了局部紧凑超群的概念的一组公理，作为群和超群的扩展，并研究了它们的基本特性。我们证明，在支持连续性上增加自然条件后，雷诺在左Haar系统上假设的公理之一会自动遵循。我们表明，紧凑的超群群的不可约表示是纤维方向的有限维。