Let \(\mathcal{C}\) be a category and \(f: A \rightarrow B\), \(g: B \rightarrow C\) morphisms for objects \(A,B,C \in \mathrm{Ob}(\mathcal{C})\).
Then there exists a morphism \(g \circ f: A \rightarrow C\), called the composition of \(g\) with \(f\).