The difference between Groupoid and Monoid
When used as nouns, groupoid means a magma: a set with a total binary operation, whereas monoid means a set which is closed under an associative binary operation, and which contains an element which is an identity for the operation.
Monoid is also adjective with the meaning: containing only one kind of metrical foot.
check bellow for the other definitions of Groupoid and Monoid
-
Groupoid as a noun (algebra):
A magma: a set with a total binary operation.
-
Groupoid as a noun (algebra, and, category theory):
A set with a partial binary operation that is associative and has inverses and identities.
Examples:
"A groupoid is a category in which every morphism is an isomorphism."
-
Monoid as a noun (mathematics):
A set which is closed under an associative binary operation, and which contains an element which is an identity for the operation.
-
Monoid as an adjective (prosody):
Containing only one kind of metrical foot.