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Mayer-Vietoris sequences in stable derivators

2014; Lehigh University; Volume: 16; Issue: 1 Linguagem: Inglês

10.4310/hha.2014.v16.n1.a15

1532-0081

Moritz Groth, Kate Ponto, Michael Shulman,

Advanced Topics in Algebra

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.