composable pair

A composable pair of morphisms in a given category CC consists of objects X,Y,ZX,Y,Z of CC and morphisms f:XYf\colon X \to Y and g:YZg\colon Y \to Z. The composite of this composable pair is the morphism gf:XZg \circ f\colon X \to Z.

A composable pair in CC is precisely a 22-simplex in the nerve of CC.

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

Last revised on September 3, 2010 at 21:01:23. See the history of this page for a list of all contributions to it.