An epic strong mono is an isomorphism. Any composite of strong monos is a strong mono. Thus f is not a strong mono. Y are two strong monos. We have to prove that w is an isomorphism.
T be the pullback of f along t .
Then u is an isomorphism as f is a strong mono. But g is a strong mono and v is a pullback of g . So v is also an isomorphism. Hence g as an intersection of isomorphisms is an isomorphism. This shows that f is a strong mono.