Limits over categories of extensions

We consider limits over categories of extensions and show how certain well-known functors on the category of groups turn out as such limits. We also discuss higher (or derived) limits over categories of extensions.Comment: 18 page

Lie Dimension Subrings

We compare, for L a Lie ring over the integers, its lower central series (\gamma_n(L))_{n>0} and its dimension series defined by \delta_n(L):=L\cap \varpi^n(L) in the universal enveloping algebra of L. We show that \gamma_n(L)=\delta_n(L) for all n<4, but give an example showing that they may differ if n=4. We introduce simplicial methods to describe these results, and to serve as a possible tool for further study of the dimension series.Comment: Small typos fixed wrt v