nLab
composable pair

A composable pair of morphisms in a given category $C$ consists of objects $X,Y,Z$ of $C$ and morphisms $f:X\to Y$ and $g:Y\to Z$. The composite of this composable pair is the morphism $g\circ f:X\to Z$.

A composable pair in $C$ is precisely a $2$-simplex in the nerve of $C$.

Sometimes one defines a composable pair to be a literal pair $(f,g)$ such that the target of $f$ is equal to the source of $g$, but this is (prima facie) evil.