category

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Contents

English [edit]

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Etymology [edit]

From Middle French categorie, from Late Latin categoria (class of predicables), from Ancient Greek κατηγορία (kategoria, head of predicables).

Pronunciation [edit]

  • IPA: /ˈkætəˌɡoɹi/
  • (file)

Noun [edit]

category (plural categories)

  1. A group, often named or numbered, to which items are assigned based on similarity or defined criteria.
    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.
  2. (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.

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Translations [edit]

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