| Stacks with a group law---or gr-stacks, or 2-groups---are known to correspond to non-abelian complexes of length 2. In a work with B. Noohi we have demonstrated that all morphisms between two gr-stacks can be conveniently encoded by diagrams of groups we call butterflies. I will explain how this allows to extend to the non-abelian case some of the properties of the derived category one encounters in homological algebra: the long exact sequence, and the cone. Time permitting, I will give an idea on how to move up in length, that is, to consider longer complexes: one has to consider more complicated diagrams, which we have called bats. |