Take the 2-minute tour ×  Let $\mathcal{C}$ be a small finitely
complete category equipped with a Grothendieck (pre)topology
$\tau$. For $\ast$ the terminal category (one object, one
morphism), denote by $i: \ast \to \mathcal{C}$ the inclusion of
the terminal object into $\mathcal{C}$. Equip $\ast$ with the
trivial topology in which the only covering is the identity
morphism of the unique object onto itself.  By the usual yoga of
functoriality of presheaves, $i$ induces a triple of adjoint
functors $i_! \dashv i^\ast \dashv i_\ast$ between the
categories of presheaves on $\mathcal{C}$ and $\ast$. Trivially
$i$ preserves coverings and is left exact —that is, it furnishes
a morphism of sites. Then $i^\ast$ takes sheaves to sheaves and
so the pair $i_! \dashv i^\ast$ descends to an adjoint pair, $a
i_! \dashv i^*$ ($a$ denoting sheafification), of functors
between the appropriate categories of sheaves, which is in fact
nothing but the geometric morphism of global sections of
$\mathrm{Sh}(\mathcal{C}, \tau)$ cons