Morphism : For every pair \(X, Y\) of objects, there is a set \(\mathbf{Hom}(X, Y)\), called the morphisms from \(X\) to \(Y\) in \(\mathbf{C}.\) If \(\boldsymbol{f}\) is a morphism from \(X\) to \(Y\), we write \(\boldsymbol{f} : X \rightarrow Y.\) 