It is well-known that a paracompact space X is of covering dimension n
if and only if any map f: X -> K from X to a simplicial complex K can be pushed 
into its n-skeleton K^{(n)}. We use the same idea to define dimension in the coarse category.
It turns out the analog of maps f: X-> K is related to asymptotically Lipschitz maps,
the analog of paracompact spaces are spaces related to Yu's  Property A,
and the dimension coincides with Gromov's asymptotic dimension.