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Groupoid vs Monoid - What's the difference?

groupoid | monoid |

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)
  • (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.
  • A groupoid is a category in which every morphism is an isomorphism.

    monoid

    English

    Noun

    (en noun)
  • (mathematics) A set which is closed under an associative binary operation, and which contains an element which is an identity for the operation.
  • Hypernyms

    * semigroup

    Hyponyms

    * group

    See also

    * * category * groupoid * loop * magma * quasigroup * submonoid

    Anagrams

    * (l) ---- ==Serbo-Croatian==

    Noun