Definition:Composition of Morphisms
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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.