Mardesic factorization theorem for asymptotic dimension

The main goal of this note is to prove a coarse analogue of Factorization Theorems in Dimension Theory: Let $f: X \rightarrow Y$ be a coarsely continuous map. Then $f$ factors through coarsely continuous maps $g : X \rightarrow Z$ and $h : Z \rightarrow Y$ with asymptotic dimension of $Z$ at most asymptotic dimension of $X$ and the weight of $Z$ at most the weight of $Y$.