For anyone interested in category theory, the description given halfway, that "the tensor product is initial in the category of multilinear maps", is honestly a

For anyone interested in category theory, the description given halfway, that "the tensor product is initial in the category of multilinear maps", is honestly almost enough information to replicate the remainder of this article (the non-computational bits anyway) I'm by no means an expert in CT, but I can now read enough of it to see that. It's kind of like back in high school physics when you knew that everything could be solved by knowing F = ma and doing a bit of algebra.