# category

EN[ˈkæɾəˌɡɒɹi] [ˈkatɪɡ(ə)ɹi]
US
WCategory
• Category, plural categories, may refer to:

## Definition of category in English Dictionary

• NounSUF-ory
1. A group, often named or numbered, to which items are assigned based on similarity or defined criteria.
1. (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.
1. One well-known category has sets as objects and functions as arrows.
2. 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.
2. More Examples
1. Used in the Middle of Sentence
• If slice category C over X has two objects (A, f) and (B, g) and a morphism h&#160;: (A, f) → (B, g), then this morphism would correspond to a like-named morphism h&#160;: A → B of C such that .
• “The dating industry has come a long way since its inception, but the category remains underpenetrated.”
• A new semisymmetrization functor, which maps the category of quasigroups with homotopies to the category of semisymmetric quasigroups with homomorphisms is given.
• Part-of-Speech Hierarchy
1. Nouns
• Countable nouns