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Template:Morphism property
Suppose C {\displaystyle {\mathcal {C}}} is a category, A , B ∈ Ob C {\displaystyle A,B\in \operatorname {Ob} {\mathcal {C}}} , and f ∈ C ( A , B ) {\displaystyle f\in {\mathcal {C}}(A,B)} . f {\displaystyle f} is termed an epimorphism, or epic, if for any object C {\displaystyle C} and any g , h ∈ C ( B , C ) {\displaystyle g,h\in {\mathcal {C}}(B,C)} we have:
g ∘ f = h ∘ f ⟹ g = h {\displaystyle g\circ f=h\circ f\implies g=h} .
is a category, 
, and 
. 
is termed an epimorphism, or epic, if for any object 
and any 
we have:
.