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