Binary Cartesian Product
A binary cartesian product in a Category
of two objects
is an object
equipped with a pair of projections
,
that satisfies the following universal property:
- For any other
equipped with maps
,
, there exists a unique universal map
such that
and
.
Properties
Global Definition
A category
has all binary cartesian products if and only if the functor
that sends an object
to
has a Right
Adjoint.