Stefanich's conjecture on limits of presentable n-categories

From papers

Let nPrn\mathsf{Pr} be the 11-category of presentable nn-categories, defined as the filtered colimit

nPr=limκnPrκn\mathsf{Pr}=\varinjlim_{\kappa}n\mathsf{Pr}^{\kappa}

where nPrκn\mathsf{Pr}^{\kappa} is the category of κ\kappa-compactly generated nn-categories, for regular cardinals κ\kappa. Stefanich's conjecture. The 11-category nPrn\mathsf{Pr} has small limits for every n0n\geq0. This problem was widely open and was posed by Stefanich as Conjecture 5.5.1; the supplied text gives no resolution.

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Sources & referencesView supporting material

Primary source

Ko Aoki, “Higher presentable categories and limits”, arXiv:2510.13503 (2025).

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