Whoops. That one slipped past. Thanks. In case it's not clear, I just specialize tensor sum to the category Set; that's all. At the end I do mention how the te

Whoops. That one slipped past. Thanks. In case it's not clear, I just specialize tensor sum to the category Set; that's all. At the end I do mention how the tensor sum applies on a wider class of objects. In fact, any Cartesian category has (finite) tensor products, even if the objects aren't traditionally thought of as "algebraic structures", e.g. certain classes of topological spaces, Frolicher manifolds, etc.