  We introduce a new asymptotic one-sided and symmetric tensor norm, the latter
of which can be considered as the minimal tensor norm on the category of
separable C*-algebras with homotopy classes of asymptotic homomorphisms as
morphisms. We show that the one-sided asymptotic tensor norm differs in general
from both the minimal and the maximal tensor norms and we discuss its relation
to semi-invertibility of C*-extensions.
