A composable pair of morphisms in a given category consists of objects of and morphisms and . The composite of this composable pair is the morphism .
A composable pair in is precisely a -simplex in the nerve of .
Sometimes one defines a composable pair to be a literal pair such that the target of is equal to the source of , but this is (prima facie) evil.
Revised on September 3, 2010 21:01:23
by Urs Schreiber