Definition:Composition of Morphisms

From ProofWiki
Jump to navigation Jump to search

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