Partially ordered sets (posets) provide a natural way of modeling problems where communication constraints between subsystems have a hierarchical or causal structure. In this talk, we consider general poset-causal decentralized decision-making problems, and describe a simple and natural controller architecture based on the Moebius transform of the poset. This architecture possesses simple and appealing separation properties. In particular, we show how our earlier results on H2-optimal decentralized control for arbitrary posets can be cast exactly into this framework, by exploiting a key separation property of the H2 norm, and the incidence algebra of the poset. Joint work with Parikshit Shah (U. Wisconsin).