 Composition : For every triple \(X, Y\) and \(Z\) of objects, there exists a partial binary operation from \(\mathbf{Hom}(X, Y) \times \mathbf{Hom}(Y, Z)\) to \(\mathbf{Hom}(X, Z)\), called the composition of morphisms in \(\mathbf{C}.\) If \(\boldsymbol{f}: X \rightarrow Y\) and \(\boldsymbol{g}: Y \rightarrow Z\), the composition of \(f\) and \(g\) is notated \((\boldsymbol{g} \circ \boldsymbol{f}): X \rightarrow Z.\)