An introduction to Grothendieck derivators

Derivators provide extensions of the more classical derived categories or
homotopy categories to a framework with a well-behaved calculus of homotopy limits.
It turns out that these homotopy limits encode many interesting constructions arising
in various areas of pure mathematics. 

In this talk we give an introduction to this calculus and sketch ideas involved in the
construction of canonical triangulations, thereby indicating that stable derivators
provide an enhancement of triangulated categories. If time allows for it, then we
conclude the talk by applications to abstract representation theory of quivers.