derived pasting scheme

Bonjour, In Kapranov & Voevodsky, "Combinatorial-geometric aspects of polycategory theory : pasting scheme and higher bruhat orders", Cahiers de topologie et géométrie différentielle catégoriques, Vol XXXII-1 (1991), the authors discuss the problem of the existence of the "derived pasting scheme" of a composable pasting scheme. I would like to know please what have been done on this subject since 1991 ? pg.