Graded tensor product
= Graded tensor product
{title2=$(a\otimes b)(c\otimes d)=(-1)^{|b||c|}ac\otimes bd$}
The tensor product of graded algebras uses the displayed multiplication, incorporating the sign for interchanging homogeneous factors. This is the algebra structure in the cohomological <Künneth theorem>, and explains the signs of mixed intersection products on product manifolds.