Given a simplicial model category (in the sense of Quillen) and a suitable abelian group object in it, one has an associated cohomology theory. In particular, if one considers an appropriate diagram category, we show this cohomology theory is the home of obstructions to rectifying homotopy commutative diagrams. Thus, one might want to try to decompose this cohomology of diagrams in terms of smaller pieces. We have two methods for attempting this decomposition, which I will describe in as much detail as time allows. This is based on joint work with David Blanc and James Turner.