\begin{definition}[Definition:Composition of Morphisms]
Let $\mathbf C$ be a metacategory.
Let $\left({g, f}\right)$ be a pair of composable morphisms.
Then the '''composition of $f$ and $g$''' is a morphism $g \circ f$ of $\mathbf C$ subject to:
:$\operatorname{dom} \left({g \circ f}\right) = \operatorname{dom} f$
:$\operatorname{cod} \left({g \circ f}\right) = \operatorname{cod} g$
This '''composition of morphisms''' can be thought of as an abstraction of both composition of mappings and transitive relations.
\end{definition}