We define term rewriting systems on the vertices and faces of nestohedra, and show that the former are confluent and terminating. While the associated poset on vertices generalizes Barnard--McConville's flip order for graph-associahedra, the preorder on faces likely generalizes the facial weak order for permutahedra. Moreover, we define and study contextual families of nestohedra, whose local confluence diagrams satisfy a certain uniformity condition. Among them are associahedra and operahedra, whose associated proofs of confluence for their rewriting systems reproduce proofs of categorical coherence theorems for monoidal categories and categorified operads.

翻译：我们定义了nestohedra顶点和面上的项重写系统，并证明了前者具有合流性和终止性。虽然顶点上的关联偏序集推广了图-associahedra的Barnard-McConville翻转序，但面上的预序很可能推广了permutahedra的面弱序。此外，我们定义并研究了nestohedra的上下文族，其局部合流图满足特定的均匀性条件。其中包含associahedra和operahedra，它们重写系统的合流性证明重现了幺半范畴和范畴化operads的范畴连贯性定理证明。