On Cofiltered Limits of $\infty$-Categories and Adjunctions

Thorger Geiß

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arXiv · 2608.06551

On Cofiltered Limits of $\infty$-Categories and Adjunctions

Thorger Geiß

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Abstract

We prove that, under mild assumptions, the limit of a cofiltered diagram of $\infty$-categories is a reflective (resp. coreflective) localization of its oplax (resp. lax) limit. This gives rise to a number of exceptional 'stability' results for categorical properties under such limits, in particular one for adjunctions. As an application, we recover a push-pull formula describing certain filtered colimits in the $\infty$-category $\mathrm{Pr}^L$ of presentable $\infty$-categories.

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Thorger Geiß. 2026-08-06. On Cofiltered Limits of $\infty$-Categories and Adjunctions. https://arxiv.org/abs/2608.06551

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