  This paper studies the asymptotic product of two metric spaces. It is well
defined if one of the spaces is visual or if both spaces are geodesic. In this
case the asymptotic product is the pullback of a limit diagram in the coarse
category. Using this product construction we can define a homotopy theory on
coarse metric spaces in a natural way. We prove that all finite colimits exist
in the coarse category.
