Homology, Homotopy and Applications

Volume 16 (2014)

Number 1

Mayer-Vietoris sequences in stable derivators

Pages: 265 – 294

DOI: http://dx.doi.org/10.4310/HHA.2014.v16.n1.a15

Authors

Moritz Groth (Department of Mathematics, Radboud University, Nijmegen, Netherlands)

Kate Ponto (Department of Mathematics, University of Kentucky, Lexington, Ky., U.S.A.)

Michael Shulman (Department of Mathematics and Computer Science, University of San Diego, California, U.S.A.)

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

derivator, homotopy exact square, Mayer-Vietoris sequence

2010 Mathematics Subject Classification

55U35

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