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Mayer-Vietoris homotopy groups sequence of a pull-back of a fibration

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Agusti Roig

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Oct 30, 2009, 5:00:02 AM10/30/09
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This must be an elementary question: could somebody tell me a
reference for the Mayer-Vietoris homotopy groups sequence of a pull-
back of a fibration?

I'm working in the category of pointed simplicial sets. So I've a pull-
back of a (Kan) fibration of pointed simplicial sets, and I've read
that in this situation you have an associated Mayer-Vietoris sequence
relating the homotopy groups of the simplicial sets of the pull-back
that looks like the classical Mayer-Vietoris sequence for the singular
homology of a pair of open sets covering a topological space.

I've been searching in May's "Simplicial objects in Algebraic
Topology" and Goerss-Jardine's "Simplicial Homotopy Theory", but I
couldn't find it.

Any hints are welcome.

Agusti Roig

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