identity morphism

Let \(\mathcal{C}\) be a category and \(A, B \in \mathrm{Ob}(\mathcal{C})\).

Then there exist morphisms \(\mathrm{id}_{A}: A \rightarrow A\) and \(\mathrm{id}_{B}: B \rightarrow B\) such that for a morphism \(f: A \rightarrow B\) follows:

\begin{align*} f =& f \circ \mathrm{id}_{A} \\ =& \mathrm{id}_{B} \circ \mathrm{id}_{B} \end{align*}