Abstracts for Abstract Homotopy Theory Seminar

Limits of ∞-categories are usually much easier to compute than colimits. Nevertheless, in Pr^L, limits and colimits indexed by a space coincide as proven by Lurie. Harpaz has shown a similar phenomenon for ∞-categories with π-finite colimits, which plays an important role in the theory of higher semiadditivity. In this talk, I will explain a common generalization of these results. Surprisingly, the proof will make use of the (∞,3)-category of iterated spans, and its universal property due to Stefanich, which encodes such ambidexterity phenomena in a coherent fashion.