Consider a proper strong subobject W of X . As L is reduced, L W is not unipotent. This implies that W is not unipotent as the pullback of any unipotent map is unipotent. The pullback of any epi along a localization is epic as any localization is coflat. Conversely assume f is not epic.
L V be the pullback of g along w .
Since um factors through the proper strong subobject L V of L , it is not epi. P be the pullback of t along p . The following commutative diagram implies that t and f are not disjoint, thus f is unipotent. Y is a localization of Y at a prime P . V s are the induced maps.