%0 Journal Article
%T A classification of 2-chains having 1-shell boundaries in rosy theories
%A Byunghan Kim
%A SunYoung Kim
%A Junguk Lee
%J Mathematics
%D 2015
%I arXiv
%X 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.
%U http://arxiv.org/abs/1503.04564v1