Epimorphicity in pushouts of normal epimorphisms

Determine whether, in a z-exact category, given a morphism of short exact sequences whose right square is a pushout of normal epimorphisms, the induced map m on the left is always an epimorphism; also formulate and resolve the dual question.

Background

The paper studies when pushouts/pullbacks of normal (co)kernels preserve exactness. This exercise asks whether epimorphicity of an induced map is guaranteed under a pushout of normal epimorphisms in a short exact diagram; the dual question concerns monomorphisms under pullbacks.