\begin{definition}[Definition:Inverse Morphism]
Let $\mathbf C$ be a metacategory.
Let $f: X \to Y$ be a morphism of $\mathbf C$.
A morphism $g: Y \to X$ is said to be an '''inverse (morphism)''' for $f$ {{iff}}:
:$g \circ f = I_X$
:$f \circ g = I_Y$
where $I_X$ denotes the identity morphism on $X$.
It follows that $f$ is an isomorphism {{iff}} it has an '''inverse morphism'''.
\end{definition}