during this talk i will introduce the notion of a k-aou space, which we may think of as a matricial archimedean order unit space. i will then describe the relationship between the category of k-aou spaces and k-positive maps, and the category of operator systems and completely positive maps. after demonstrating the existence of injective envelopes and c*-envelopes in the category of k-aou spaces, i will describe a connection with quantum correlations. combined with previous work, this yields a reformulation of tsirelson's conjecture.