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Grothendieck spectral sequence (cohomology version) for posets with functor coefficient

In this paper, Quillen mentioned a spectral sequence as follows. Let $f:X\to Y$ is a poset map and $\mathcal{F}:X\to Ab$, where $Ab$ is the category of abelian groups, a functor which is contravariant ...
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Generalising the Mayer-Vietoris principle

My understanding of the general Mayer-Vietoris principle is as follows. We want to compute the cohomology of some sheaf $\mathscr{F}$. We start by taking a resolution $$\mathscr{F}_0 \rightarrow \...
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