Twisted Coefficients on coarse Spaces and their Corona

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