Definition 0.1
A morphism e : A → B {\displaystyle e:A\to B} is an epimorphism if for any two morphisms f , g : B → C {\displaystyle f,g:B\to C} , f ∘ e = g ∘ e {\displaystyle f\circ e=g\circ e} implies f = g {\displaystyle f=g} .