Groupoid vs Monoid - What's the difference?
groupoid | monoid |
(algebra) A magma: a set with a total binary operation.
(algebra, and, category theory) A set with a partial binary operation that is associative and has inverses and identities.
(mathematics) A set which is closed under an associative binary operation, and which contains an element which is an identity for the operation.
As nouns the difference between groupoid and monoid
is that groupoid is a magma: a set with a total binary operation while monoid is a set which is closed under an associative binary operation, and which contains an element which is an identity for the operation.groupoid
English
Noun
(en noun)- A groupoid is a category in which every morphism is an isomorphism.