Fundamentals of Compositional Rewriting Theory

A foundational theory of compositional categorical rewriting is presented, based on a collection fibration-like properties that collectively induce and intrinsically structure the large lemmata used in proofs theorems such as concurrency associativity. The resulting highly generic these are given. It noteworthy proof theorem takes only few lines and, while associativity remains somewhat longer, it would be unreadably long if written directly terms basic lemmata. In essence, our framework improves readability ease comprehension by exposing latent modularity. curated list known instances to conclude paper with detailed discussion conditions under which Double Pushout Sesqui-Pushout semantics graph transformation compositional.