Abstract Coarse geometry, and in particular coarse homotopy theory, has proven to be a powerful tool for approaching problems geometric group theory higher index theory. In this paper,we continue develop area by proving Lifting Lemma with respect certain class of bornologous surjective maps. This is wide enough include quotients coarsely discontinuous actions, which allows us obtain results con...

A certain Grothendieck topology assigned to a metric space gives rise sheaf cohomology theory which sees the coarse structure of space. Already constant coefficients produce interesting groups. In degree 0, they see number ends this paper, resolution via cochains is developed. It serves be valuable tool for computing cohomology. addition, homotopy invariance with established. This property can ...