English

Mayer-Vietoris sequences in stable derivators

Category Theory 2013-12-20 v2 Algebraic Geometry Algebraic Topology

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.

Keywords

Cite

@article{arxiv.1306.2072,
  title  = {Mayer-Vietoris sequences in stable derivators},
  author = {Moritz Groth and Kate Ponto and Michael Shulman},
  journal= {arXiv preprint arXiv:1306.2072},
  year   = {2013}
}

Comments

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

R2 v1 2026-06-22T00:30:47.413Z