  We classify, in a non-trivial 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.
