  Sesqui-pushout (SqPO) rewriting along non-linear rules and for monic matches
is well-known to permit the modeling of fusing and cloning of vertices and
edges, yet to date, no construction of a suitable concurrency theorem was
available. The lack of such a theorem, in turn, rendered compositional
reasoning for such rewriting systems largely infeasible. We develop in this
paper a suitable concurrency theorem for non-linear SqPO-rewriting in
categories that are quasi-topoi (subsuming the example of adhesive categories)
and with matches required to be regular monomorphisms of the given category.
Our construction reveals an interesting "backpropagation effect" in computing
rule compositions. We derive in addition a concurrency theorem for non-linear
double pushout (DPO) rewriting in rm-adhesive categories. Our results open
non-linear SqPO and DPO semantics to the rich static analysis techniques
available from concurrency, rule algebra and tracelet theory.
