theorem :: CAT_1:36

for C being Category
for a, b being Object of C
for f being Morphism of a,b st Hom (a,b) <> {} holds
( f is epi iff for c being Object of C
for g1, g2 being Morphism of b,c st Hom (b,c) <> {} & g1 * f = g2 * f holds
g1 = g2 ) ;