A triangulated category admits a strong generator if, roughly speaking,
every object can be built in a globally bounded number of steps starting
from a single object and taking iterated cones. The importance of
strong generators was demonstrated by Bondal and van den Bergh, who
proved that the existence of such objects often gives you a
representability theorem for cohomological functors. The importance was
further emphasised by Rouquier, who introduced the dimension of
triangulated categories, and tied this numerical invariant to the
representation dimension. In this talk I will discuss the generation
time for strong generators (the least number of cones required to build
every object in the category) and a refinement of the dimension which is
due to Orlov: the set of all integers that occur as a generation time.
After introducing the necessary terminology, I will focus on categories
occurring in representation theory and explain how to compute this
invariant for the bounded derived category of the path algebras of type
A and D, as well as the corresponding cluster categories.