A strict factorization system is like an orthogonal factorization system, but the factorizations are specified uniquely on the nose, rather than merely up to isomorphism.
One reason these are of interest is that they can be identified with distributive laws in the bicategory of spans, as shown in
Ordinary orthogonal factorization systems can be similarly characterized by:
using a type of pseudo distributive law?, as in the above paper;
by working in the bicategory of profunctors instead, as in this paper (see also factorization system over a subcategory); or by
using weak distributive law?s, as in this paper.