> For vector spaces, the sum operation is the Cartesian product and the product operation is the tensor product. For vector spaces the sum operation is the Car

> For vector spaces, the sum operation is the Cartesian product and the product operation is the tensor product. For vector spaces the sum operation is the Cartesian product, and the product operation is also the Cartesian product (at least for finite many vector spaces). C.f. https://math.stackexchange.com/questions/1910808/prove-that-v-%e2%8a%95w-can-be-made-into-both-a-product-of-v-and-w-and-a-coprod https://math.stackexchange.com/questions/1910808/prove-that-...