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How would one show a morphism is an epimorphism iff it is surjective (ONTO)?
An epimorphism in category theory is a morphism ##f:X\rightarrow Y## such that if ##g,h:Y\rightarrow Z## are morphisms such that ##g\circ f = h\circ f##, then ##g=h##.What is your definition of epimorphism if it's not that it is a surjective map?