for C1, C2, A, B being category
for P1 being Functor of A,C1
for P2 being Functor of A,C2
for Q1 being Functor of B,C1
for Q2 being Functor of B,C2 st P1 is covariant & P2 is covariant & Q1 is covariant & Q2 is covariant & A,P1,P2 is_product_of C1,C2 & B,Q1,Q2 is_product_of C1,C2 holds
A ~= B