Weak memory models determine the behavior of concurrent programs. While they are often understood in terms of reorderings that the hardware or the compiler may perform, their formal definitions are typically given in a very different style—either axiomatic or operational. In this paper, we investigate to what extent weak behaviors of existing memory models can be fully explained in terms of reo...

The theory of operads, defined through categories of labeled graphs, is generalized to suit definitions of higher categories with arbitrary basic shapes. Constructions of cubical, globular and opetopic weak higher categories are obtained as examples.