Since the analytic category is strict, these factorization can be glue together to obtain a global factorization for t by f . n Proposition 5.5.7. A mono is a local isomorphism iff it is a fraction. Thus u is normal. So we only need to prove that u is coflat. Since the class of local isomorphisms is closed under pullback, it suffices to prove that u is precoflat.
T is the pullback of f and t .
This shows that r is epic, which means that u is precoflat as desired.