> the tensor product is not the category theoretical product in Vect. Oh, you're right and I'm a twit. (Not simply because I got it wrong, but because if I'd s

> the tensor product is not the category theoretical product in Vect. Oh, you're right and I'm a twit. (Not simply because I got it wrong, but because if I'd spent 30 seconds to think what the product construction does in Vect rather than relying on my plainly-unreliable memory, it would have been obvious that it isn't the tensor product: there are obviously no candidates for the required projection morphisms.) Thanks! (And apologies to Jeremy for having made an invalid argument, though in fact I think the arguments "the product is the tensor product, the cartesian product is actually a coproduct, so they're very different" and "the product is the cartesian product, the tensor product is an entirely different kind of product, so they're very different" are about equally convincing modulo the fact that the first one's key premise turns out to be false.)