  In this paper, we study internal properties of a Cosserat media. In fact, by
using groupoids and smooth distributions, we obtain a three canonical
equations. The \textit{non-holonomic material equation for Cosserat media}
characterizes the uniformity of the material. The \textit{holonomic material
equation for Cosserat media} permits us to study when a Cosserat material is a
second-grade material. It is remarkable that these two equations also provide
us a unique and maximal division of the Cosserat medium into uniform and
second-grade parts, respectively. Finally, we present a proper definition of
homogeneity of the Cosserat medium, without assuming uniformity. Thus, the
\textit{homogeneity equation for Cosserat media} characterizes this notion of
homogeneity.
