 A particularly fruitful approach of this kind, due to Abramsky and Coecke [2009] takes a physical theory to be represented by a symmetric monoidal category—roughly, a category equipped with a naturally symmetric and associative tensor product. Subject to some further constraints (e.g., compact closure), such categories exhibit formal properties strikingly reminiscent of quantum mechanics. Interestingly, it has recently been shown by Harding [2009] that, in every strongly compact closed category with biproducts, every object is associated with an orthomodular poset Proj\((A)\) of “weak projections”, and that Proj\((A \otimes B)\) behaves in many respects as a sensible tensor product for Proj\((A)\) and Proj\((B)\). From this perspective, the FR example simply exhibits a pathological example — \(A_5\) and the state \(\alpha\) — that can not be accommodated in such a theory, establishing that the monoidality requirement imposes a nontrivial restriction on the structure of individual systems. 