Definition:Composition of Morphisms

Definition
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.

Also see

 * Composable Morphisms
 * Metacategory