Filter quotients and non-presentable \((\infty,1)\)-toposes (Q2040521)

The author defines filter quotients of \((\infty,1)\)-categories and proves that filter quotients preserve the structure of an elementary \((\infty,1)\)-topos and in particular lift the filter quotient of the underlying elementary topos. The construction is then specialized to the case of filter products of \((\infty,1)\)-categories and the author proves a characterization theorem for equivalences in a filter product. Then he uses filter products to construct a large class of elementary \((\infty,1)\)-toposes that are not Grothendieck \((\infty,1)\)-toposes. Moreover, he gives one detailed example for the interested reader who would like to see how it is possible to construct such an \((\infty,1)\)-category, but would prefer to avoid the technicalities regarding filters.