  We recall Schur's work on universal central extensions and develop the
analogous theory for categorical extensions of groups. We prove that the String
2-groups are universal in this sense and study in detail their restrictions to
the finite subgroups of the Spin groups. Of particular interest are subgroups
of the 3-sphere Spin(3), as well as the spin double covers of the alternating
groups, whose categorical extensions turn out to be governed by the stable
3-stem.

Category Theory;Algebraic Topology