DEFINITION 09.2
Let

be a (not necessarily commutative) ring.
Let

be a right

-module. Let

be a left

-module.
Then for any module

, a map

is said to
be an

-balanced biadditive map if it
satisfies the following conditions.
-
-
-
Universality argmuments are deeply related to the uniqueness of initial objects.
Consult Lang “Algebra”.