
TL;DR
This paper proves a unifying ambidexterity result for certain $infty$-categories, extending known phenomena and employing Stefanich's universal property to encode ambidexterity coherently.
Contribution
It introduces a general ambidexterity theorem for $infty$-categories with colimits, unifying previous results and employing a novel proof technique.
Findings
Unifies limits and colimits in presentable $infty$-categories.
Extends $infty$-semiadditivity to broader contexts.
Provides a new proof approach using Stefanich's universal property.
Abstract
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 -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.
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Taxonomy
TopicsCognitive Science and Mapping
