This paper contains preliminary steps in demonstrating how the Dempster Shafer theory can be placed into the framework of category theory. In the Dempster Shafer setting, the elements of the base set of a probability space are, typically, subsets of some set. Consequently, the elements of the corresponding sigma algebra are not subsets of a set, but rather, subsets of subsets of a set. A probability function, in this case, no longer has the classical meaning. This situation lends itself to the more general notions of inner and outer measures, which Shafer calls belief and plausibility, respectively. The categorical approach attempts to unify classical and non-classical concepts into a setting, so that, depending on the nature of the stochastic problem at hand, a general framework may be specialized appropriately to attack the problem.