??what are the formal properties of a map f : r1 X r2 -> r3 corresponding to a homomorphism from the tensor product of r1 and r2 ?? ... and so forth...

??came up because i was thinking about tensor product of finitely cocomplete algebroids, vs "hom-wise" tensor product of their underlying algebroids, vs cartesian product of their underlying algebroids... ??something about representing bi-[cokernel-preserving]-k-linear functor in terms of each of these... ???or something???....