Category (category theory)
A category, , is a mathematical object consisting of:
- A class, of objects.
- For every pair of objects , a class of morphisms from to . (We sometimes write to mean .)
- For every three objects, , a binary operation called composition, which satisfies:
- (associativity) Given , and we have
- (identity) For and object , there is an identity morphism such that for any :
The class of all morphisms of is denoted .
A category is called small if both and are sets. If is not small, then it is called large. is called locally small if is a set for all . Most important categories in math are not small, but are locally small. This article is a stub. Help us out by .