What is an ∞-topos?

Alexander Campbell – 13 October 2021

In this expository talk, we will review three characterisations of ∞-topoi from Chapter 6 of Lurie's book on Higher Topos Theory: (1) as accessible left-exact localisations of presheaf ∞-categories, (2) as ∞-categories satisfying higher categorical analogues of Giraud's axioms, and (3) as locally presentable ∞-categories in which all colimits obey the descent principle.