Definition:Groupoid (Universal Algebra)
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Definition
Let $G$ be a class.
Let $\ast: G \times G \to G$ be a binary operation on $G$.
An algebra $\left({G, \ast}\right)$ is called a groupoid iff $\ast$ is the only binary operation on $G$.
What is an algebra in this context?
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If the $G$ is a small class then $\left({G, \ast}\right)$ is called a magma.
Sources
- Stanley Burris and H. P. Sankappanavar: A Course in Universal Algebra (1981): $\text {II} \ \S 1$
