Pullback stability of abelian image factorization
= Pullback stability of abelian image factorization
Pull back the two arrows of an <image factorization in an abelian category>. <Monomorphisms> are preserved by pullback, and <pullback stability of epimorphisms in an abelian category> preserves its epic part. Pasting the squares gives the pulled-back composite. The resulting epi-mono factorization is therefore its image factorization by uniqueness.