bn:03334078n
Noun Concept
Categories: long volume value, Category theory, Algebraic structures
EN
category  abstract category  large category  locally small  locally small category
EN
In mathematics, a category is a collection of "objects" that are linked by "arrows". Wikipedia
English:
math
category theory
mathematics
maths
Definitions
Examples
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Sources
EN
In mathematics, a category is a collection of "objects" that are linked by "arrows". Wikipedia
A structure consisting of objects and arrows Wikipedia Disambiguation
Algebraic structure of objects and morphisms between objects, which can be associatively composed if the domains agree Wikidata
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. Wiktionary
EN
One well-known category has sets as objects and functions as arrows. Wiktionary
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. Wiktionary