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Category vs Monoid - What's the difference?

category | monoid |

In mathematics terms the difference between category and monoid

is that category is a collection of objects, together with a transitively closed collection of composable arrows between them, such that every object has an identity arrow, and such that arrow composition is associative 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.

As nouns the difference between category and monoid

is that category is a group, often named or numbered, to which items are assigned based on similarity or defined criteria 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.

category

Noun

(categories)
  • A group, often named or numbered, to which items are assigned based on similarity or defined criteria.
  • *
  • The traditional way of describing the similarities and differences between constituents is to say that they belong to categories'' of various types. Thus, words like ''boy'', ''girl'', ''man'', ''woman'', etc. are traditionally said to belong to the category''' of Nouns, whereas words like ''a'', ''the'', ''this'', and ''that'' are traditionally said to belong to the ' category of Determiners.
    This steep and dangerous climb belongs to the most difficult category .
    I wouldn't put this book in the same category as the author's first novel.
  • (mathematics) A collection of objects, together with a transitively closed collection of composable arrows between them, such that every object has an identity arrow, and such that arrow composition is associative.
  • One well-known category has sets as objects and functions as arrows.
    Just as a monoid consists of an underlying set with a binary operation "on top of it" which is closed, associative and with an identity, a category consists of an underlying digraph with an arrow composition operation "on top of it" which is transitively closed, associative, and with an identity at each object. In fact, a category's composition operation, when restricted to a single one of its objects, turns that object's set of arrows (which would all be loops) into a monoid.

    Synonyms

    * (group to which items are assigned) class, family, genus, group, kingdom, order, phylum, race, tribe, type * See also

    Derived terms

    * category mistake * category theory * conceptual category * perceptual category * subcategory * supercategory

    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