The natural nerve model-structure conjecture for strict n-categories

From papers

Let nn be a nonnegative integer, let nC ⁣atn\mathcal{C}\!\mathit{at} denote the category of strict nn-categories, and let

Nn ⁣:nC ⁣atS ⁣ettΔopN^{\natural}_n\colon n\mathcal{C}\!\mathit{at}\to\mathcal{S}\!\mathit{et}^{t\Delta^{\operatorname{op}}}

be the natural nn-nerve, with S ⁣ettΔop\mathcal{S}\!\mathit{et}^{t\Delta^{\operatorname{op}}} the category of marked simplicial sets with the Riehl--Verity model structure for (,n)(\infty,n)-categories. Natural nerve model-structure conjecture. The model structure on nC ⁣atn\mathcal{C}\!\mathit{at} is right-transferred from the Riehl--Verity model structure on S ⁣ettΔop\mathcal{S}\!\mathit{et}^{t\Delta^{\operatorname{op}}} along NnN^{\natural}_n. This would provide the desired homotopical model for strict nn-categories and relate their categorical equivalences to the (,n)(\infty,n)-categorical model structure; the source presents it as a conjecture to be proved in forthcoming work.

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Sources & referencesView supporting material

Primary source

Viktoriya Ozornova and Martina Rovelli, “Nerves of 2-categories and 2-categorification of (,2)-categories”, arXiv:1902.05524 (2019).

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