Mayer-Vietoris sequences in stable derivators

Abstract

We show that stable derivators, like stable model cate- gories, admit Mayer-Vietoris sequences arising from cocartesian squares. Along the way we characterize homotopy exact squares and give a detection result for colimiting diagrams in derivators. As an application, we show that a derivator is stable if and only if its suspension functor is an equivalence.