Then k is a regular epi. Let f', m', n', k', g' be the images of f, m, n, k, g respectively by the pullback functor along f . The morphism f' is a split epi, therefore is a regular epi. Also f is coflat implies that k' is epic. Hence Y is the fibre product of f and g .
T be the kernel pair of f .
But f is universal epic implies that w is epic. A coherent analytic category is strict iff any finite analytic cover is extremal. A mono in a strict coherent analytic geometry is direct iff it is strong and analytic. Thus V is a direct mono.