Higher Cech theory, by Tibor Beke
We introduce a notion of `cover of level n' for a topological space, or
more generally any Grothendieck site, with the key property that
simplicial homotopy classes computed along the filtered diagram of
n-covers biject with global homotopy classes when the target is an n-type.
When the target is an Eilenberg-MacLane sheaf, this specializes to
computing derived functor cohomology, up to degree n, via simplicial
homotopy classes taken along n-covers. Our approach is purely simplicial
and combinatorial.
Tibor Beke <tbeke@umich.edu>