# Groupoids and hypergroups

There are two generalizations of usual groups: groupoids, where the multiplication operation becomes "partial", and hypergroups, for which the result of multiplying two elements is a probability measure rather than a single element. I am interested in the structure combining both these features (it might have been called "hypergroupoid", but apparently this term is already in use): multiplication is partial and obeys the same rules as in a groupoid, but its result is a probability measure on morphisms with the appropriate source and target objects. Any references?

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