Generation time for biexact functors and Koszul objects in triangulated categories

This paper concerns the generation time that measures the number of cones necessary to obtain an object in a triangulated category from another object. This invariant is called level. We establish level inequalities for enhanced triangulated categories: One inequality concerns biexact functors of topological triangulated categories, another Koszul objects. In particular, this extends inequalities for the derived tensor product from commutative algebra to enhanced tensor triangulated categories. We include many examples.