Presheaf topos
= Presheaf topos
Every <presheaf category> is a <topos>. Finite limits are pointwise; the exponential is
$$
(G^F)(C)=\operatorname{Nat}(yC\times F,G),
$$
and the <subobject classifier> assigns to $C$ the set of sieves on $C$.
= Presheaf topos
Every <presheaf category> is a <topos>. Finite limits are pointwise; the exponential is
$$
(G^F)(C)=\operatorname{Nat}(yC\times F,G),
$$
and the <subobject classifier> assigns to $C$ the set of sieves on $C$.