Lax orthogonal factorisations in monad-quantale-enriched categories - Clementino, Maria Manuel (2017)
We show that, for a quantale V and a Set-monad T laxly extended to V-Rel, the presheaf monad on the category of (T,V)-categories is simple, giving rise to a lax orthogonal factorisation system (lofs) whose corresponding weak factorisation system has embeddings as left part. In addition, we present presheaf submonads and study the LOFSs they deﬁne. This provides a method of constructing weak factorisation systems on some well-known examples of topological categories over Set.