A simplicial approach to factorization systems and Kurosh–Amitsur radicals

Regarding categories as simplicial sets via the nerve functor, we extend the notion of a factorization system from morphisms in a category, to 1-simplexes in an arbitrary simplicial set. Applied to what we call the simplicial set of short exact sequences, it gives the notion of Kurosh–Amitsur radical. That is, we present a unified approach to factorization systems and radicals.