# category

EN[ˈkæɾəˌɡɒɹi] [ˈkatɪɡ(ə)ɹi]US

WCategory

- Category, plural categories, may refer to:

- NounPLcategoriesSUF-ory
- A group, often named or numbered, to which items are assigned based on similarity or defined criteria.
- (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.

- One well-known

- A group, often named or numbered, to which items are assigned based on similarity or defined criteria.
- More Examples
- Used in the Middle of Sentence
- If slice
**category**C over X has two objects (A, f) and (B, g) and a morphism h : (A, f) → (B, g), then this morphism would correspond to a like-named morphism h : 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.

- If slice

- Used in the Middle of Sentence

## Definition of __category__ in English Dictionary

- Part-of-Speech Hierarchy
- Nouns
- Countable nouns

- Countable nouns

- Nouns

Source: Wiktionary

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