Universal property of an inverse image sheaf
= Universal property of an inverse image sheaf
{title2=$\mathcal G\to f_*f^{-1}\mathcal G$}
Every <f-morphism of sheaves> from $\mathcal G$ to $\mathcal F$ factors uniquely through the canonical f-morphism from $\mathcal G$ to its <inverse image sheaf>. A local inverse-image section is represented by sections of $\mathcal G$ on image neighbourhoods; their prescribed images glue in $\mathcal F$.