Proper morphisms of infinity-topoi


We characterise proper morphisms of infinity-topoi in terms of a relativised notion of compactness. We show that a geometric morphism of infinity-topoi is proper if and only if it commutes with colimits indexed by filtered internal infinity-categories in the target. In particular, our result implies that for any infinity-topos, the global sections functor is proper if and only if it preserves filtered colimits.

ArXiv preprint
Louis Martini
Louis Martini
PhD fellow in mathematics

I am a fourth year PhD student in the Department of Mathematical Sciences at the Norwegian University of Science and Technology in Trondheim, Norway.