To say that C is a category with (functoral) multiplication means that there is a functor ⊗ : C → C called the multiplication where C is the category of pairs of objects and pairs of morphisms from C. [More technically, C is the category of functors and natural transformations from 2 to C where 2 is the category with objects 0 and 1, and the only morphisms are the identity morphisms.] Examples of functoral multiplications are cross products, tensor products, free products and so forth on those… CONTINUE READING