Example 2

Let B be a topological space, $\mathscr{B}$ a basis of the topology of B, $\mathscr{F}= (\mathscr{F}(U), f_{UV})$ a presheaf on B relative to $\mathscr{B}$ and $\mathscr{L}= (\mathscr{L}(U))$ a subpresheaf of $\mathscr{F}$. For every open set $U\in \mathscr{B}$, denote by $i_U$ the canonical injection of $\mathscr{L}(U)$ into $\mathscr{F}(U)$. Then $i= (i_U)_{U\in\mathscr{B}}$ is a morphism of presheaves from $\mathscr{L}$ into $\mathscr{F}$. We say that $i$ is the canonical morphism from $\mathscr{L}$ into $\mathscr{F}$.