Twisted Coefficients on coarse Spaces and their Corona

To a metric space $X$ we associate a compact topological space $ u X$ called the corona of $X$. Then a coarse map $f:Xto Y$ between metric spaces is mapped to a continuous map $ u f: u Xto u Y$ between coronas. Sheaf cohomology on coarse spaces has been introduced in arXiv:1710.06725. We show the functor $ u$ preserves and reflects sheaf cohomology.