2024/11/26 by Ben-Moshe, Shay
#Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2411.17281
We prove an ambidexterity result for ∞-categories of ∞-categories admitting a collection of colimits. This unifies and extends two known phenomena: the identification of limits and colimits of presentable ∞-categories indexed by a space, and the ∞-semiadditivity of the ∞-category of ∞-categories with π-finite colimits proven by Harpaz. Our proof employs Stefanich's universal property for the higher category of iterated spans, which encodes ambidexterity phenomena in a coherent fashion.