\begin{definition}[Definition:Epimorphism (Category Theory)]
Let $\mathbf C$ be a metacategory.
An '''epimorphism''' is a morphism $f \in \mathbf C_1$ such that:
: $g \circ f = h \circ f \implies g = h$
for all morphisms $g, h \in \mathbf C_1$ for which these compositions are defined.
That is, an '''epimorphism''' is a morphism which is right cancellable. 
One writes $f: C \twoheadrightarrow D$ to denote that $f$ is an '''epimorphism'''.
\end{definition}