associativity of function composition

1. Proposition

Let \(A,B,C,D\) be sets and \(f: A \rightarrow B, g: B \rightarrow C, h: C \rightarrow D\) be maps. Then

\begin{align*} (f \circ g) \circ h =& f \circ (g \circ h) \end{align*}

i.e. composition of maps is associative.

2. Proof

Date: nil

Author: Anton Zakrewski

Created: 2024-10-13 So 18:15