Does there exist a strong factorization system on $\mathbf{Set}$ i.e. one w.f.s. in which the liftings are unique ? What are all the possibilities for these strong factorization systems ?
2026-04-25 23:03:19.1777158199
a strong factorization system on $\mathbf{Set}$
68 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
Yes, $(Epi, Mono)$ is such an example. Try to prove the axioms, it's pretty instructive! (I'm not sure about the fact that you might need some form of axiom of choice)
As for the question how to find "all" WFS on a category, I think it's an open problem even in smaller, simpler categories than $Set$.
But I'd be glad to learn I'm wrong!