 Every Grothendieck topos is an elementary topos, but the converse is not true (since every Grothendieck topos is cocomplete, which is not required from an elementary topos).The categories of finite sets, of finite "G"-sets (actions of a group "G" on a finite set), and of finite graphs are elementary topoi that are not Grothendieck topoi.If "C" is a small category, then the functor category Set"C" (consisting of all covariant functors from "C" to sets, with natural transformations as morphisms) is a topos.