"In more elementary terms, f:X???Yf: X o Y is an epimorphism if, given any g,h:Y???Zg, h: Y o Z, such that the composites ???f???g=???f???h\\stackrel{f}{ o} \\stackrel{g}{ o} = \\stackrel{f}{ o} \\stackrel{h}{ o} are equal, then already g=hg = h:" . . . .