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