Groupoid

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The term groupoid has two different meanings in mathematics. The meanings are unrelated except for the fact that both are generalizations of the concept of a group.

1). In category theory, a groupoid is a category in which every morphism is invertible. If the morphisms form a set (rather than a proper class) and there is only one object, then the groupoid can be considered as a group, with the elements of the group being the morphisms. If there is more than one object, then the groupoid is like a group with a multiplication that is only partially defined.

2). A groupoid is a set with a binary operation on it. Particular types of groupoid include semigroups, monoids, groups and quasigroups.