Partial groupoid

Group-like structures
Total Associative Identity Divisible Commutative
Partial magma UnneededUnneededUnneededUnneededUnneeded
Semigroupoid UnneededRequiredUnneededUnneededUnneeded
Small category UnneededRequiredRequiredUnneededUnneeded
Groupoid UnneededRequiredRequiredRequiredUnneeded
Magma RequiredUnneededUnneededUnneededUnneeded
Quasigroup RequiredUnneededUnneededRequiredUnneeded
Unital magma RequiredUnneededRequiredUnneededUnneeded
Loop RequiredUnneededRequiredRequiredUnneeded
Semigroup RequiredRequiredUnneededUnneededUnneeded
Monoid RequiredRequiredRequiredUnneededUnneeded
Group RequiredRequiredRequiredRequiredUnneeded
Abelian group RequiredRequiredRequiredRequiredRequired

In abstract algebra, a partial groupoid (also called halfgroupoid, pargoid, or partial magma) is a set endowed with a partial binary operation.

A partial groupoid is a partial algebra.

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