The projective dimension of $M \otimes_R N$ is bound above by the sum of the projective dimensions of the $R$-modules $M$ and $N$. There is a similar relationship for the Loewy length of the tensor product and the modules over a local ring. Both the projective dimension and the Loewy length are instances of level, an invariant that measures the number of cones necessary to obtain a module, or complex, from the ring or the residue field. I will present a result generalizing the above inequalities to enhanced triangulated categories. I will further present applications to Koszul objects, which generalize Koszul complexes. This is joint work with Marc Stephan.