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

This is the authors' abstract. We don't add key points for this paper.

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