1. A mathematical structure consisting of a set with a binary operation that is closed but not necessarily associative, commutative, or having an identity element.
Usage: mathematics; formal
2. In category theory, a small category in which every morphism is an isomorphism.
Usage: mathematics; advanced; category theory

Examples

• A groupoid is more general than a group because it does not require associativity.
• In abstract algebra, students learn that every group is a groupoid, but not every groupoid is a group.
• The fundamental groupoid of a topological space extends the concept of the fundamental group.
• Groupoids appear naturally in the study of symmetries and transformations in modern mathematics.