Mayer-Vietoris sequences in stable derivators

Abstract

We show that stable derivators, like stable model categories, 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.

This paper is a revision of the first sections of arXiv:1212.3277. v2: final version, to appear in HHA. Main proof improved after suggestion by the referee