Definition:Composable Morphisms

Definition

Let $\mathbf C$ be a metacategory.

Let $f, g \in \mathbf C_1$ be morphisms of $\mathbf C$.

Then $f$ is said to be composable with $g$ if and only if:

$\Cdm f = \Dom g$

that is, if and only if the codomain of $f$ is the domain of $g$.

When the order of composition is to be made more explicit, one says that $\tuple {g, f}$ is a composable pair.

The collection of all such composable pairs in $\mathbf C$ is denoted $\mathbf C_2$.

Also see

• Morphism
• Metacategory