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

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.

Revised on September 3, 2010 21:01:23
by Urs Schreiber
(134.100.32.208)