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
:
- (associativity) Given
The class of all morphisms of is denoted
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