We classify, in a nontrivial amenable collection of functors, all 2-chains up to
the relation of having the same 1-shell boundary. In particular, we prove that
in a rosy theory, every 1-shell of a Lascar strong type is the boundary of some
2-chain, hence making the 1st homology group trivial. We also show that, unlike
in simple theories, in rosy theories there is no upper bound on the minimal
lengths of 2-chains whose boundary is a 1-shell.