The tensor product functor 
, for a module 
over a commutative unit
ring 
,
is a covariant functor from the category
of 
-modules to itself. It maps every 
-module 
to 
and every module
homomorphism 
to the module homomorphism
 |
defined by
 |
The tensor product functor 
is defined similarly (Stacks Project Authors 2026).
