Filter Quotients and Non-Presentable $(infty,1)$-Toposes

We define filter quotients of $(infty,1)$-categories and prove that filter quotients preserve the structure of an elementary $(infty,1)$-topos and in particular lift the filter quotient of the underlying elementary topos. We then specialize to the case of filter products of $(infty,1)$-categories and prove a characterization theorem for equivalences in a filter product. Then we use filter products to construct a large class of elementary $(infty,1)$-toposes that are not Grothendieck $(infty,1)$-toposes. Moreover, we give one detailed example for the interested reader who would like to see how we can construct such an $(infty,1)$-category, but would prefer to avoid the technicalities regarding filters.