Let us consider an abelian category ${\displaystyle {\mathcal {C}}}$. Then, an object ${\displaystyle G}$ of ${\displaystyle {\mathcal {C}}}$ is called a generator if ${\displaystyle Hom_{\mathcal {C}}(G,A)}$ is nonzero for every nonzero object ${\displaystyle A}$ of ${\displaystyle {\mathcal {C}}}$.