  This paper examines the string topology category of a manifold, defined by
Blumberg, Cohen and Teleman. Since the string topology category is a
subcategory of a compactly generated triangulated category, the machinery of
stratification, constructed by Benson, Krause and Iyengar, can be applied in
order to gain an understanding of the string topology category. It is shown
that an appropriate stratification holds when the manifold in question is a
simply connected compact Lie group. This last result is used to derive some
properties of the relevant string topology categories.
