Categorical Ambidexterity

Fuente: arXiv
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Main Author: Ben-Moshe, Shay
Format: Preprint
Published: 2024
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author Ben-Moshe, Shay
author_facet Ben-Moshe, Shay
contents We prove an ambidexterity result for $\infty$-categories of $\infty$-categories admitting a collection of colimits. This unifies and extends two known phenomena: the identification of limits and colimits of presentable $\infty$-categories indexed by a space, and the $\infty$-semiadditivity of the $\infty$-category of $\infty$-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.
format Preprint
id arxiv_https___arxiv_org_abs_2411_17281
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Categorical Ambidexterity
Ben-Moshe, Shay
Category Theory
Algebraic Topology
18N60, 18A30, 18N65
We prove an ambidexterity result for $\infty$-categories of $\infty$-categories admitting a collection of colimits. This unifies and extends two known phenomena: the identification of limits and colimits of presentable $\infty$-categories indexed by a space, and the $\infty$-semiadditivity of the $\infty$-category of $\infty$-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.
title Categorical Ambidexterity
topic Category Theory
Algebraic Topology
18N60, 18A30, 18N65
url https://arxiv.org/abs/2411.17281