Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Rings associated with pairs of groups

We introduce the notion of a groupoid with an additional structure called "$\Delta$-structure", and construct two pairs of adjoint functors between the category of $\Delta$-groupoids and the category of rings. It will be shown on few examples that these adjunctions are non-trivial. Then, for any pair of groups $H\subset G$ we associate a $\Delta$-groupoid. One application of this construction is the possibility of composing with the above functors to obtain ring-valued invariants of group pairs.