# PlanetPhysics/Generator

Let us consider an abelian category . Then, an object of is called a *generator* if is nonzero for every nonzero object of .

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