nLab composable pair

A composable pair of morphisms in a given category CC consists of objects X,Y,ZX,Y,Z of CC and a pair of 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 2-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 violates the principle of equivalence

Last revised on October 3, 2021 at 05:19:12. See the history of this page for a list of all contributions to it.