A category is a collection of objects
with a collection of morphisms
with the following properties
- Each morphism
has a domain
and codomain
. We write
.
- Each object
has an identity morphism
.
- For any morphisms
there exists a composite morphism
- For any
, both
and
are equal to
.
- For any composable triple of morphisms
,
,
, the composition is associative, e.g
. We will denote it by
We will often call morphisms arrows.