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

  1. Groupoid as a noun (algebra):

    A magma: a set with a total binary operation.

  2. 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."

  1. 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.

  1. Monoid as an adjective (prosody):

    Containing only one kind of metrical foot.