Filter quotients and non-presentable (∞,1)-toposes

We define filter quotients of -categories and prove that filter quotients preserve the structure of an elementary -topos and in particular lift the filter quotient of the underlying elementary topos. We then specialize to the case of filter products of -categories and prove a characterization theorem for equivalences in a filter product. Then we use filter products to construct a large class of elementary -toposes that are not Grothendieck -toposes. Moreover, we give one detailed example for the interested reader who would like to see how we can construct such an -category, but would prefer to avoid the technicalities regarding filters.