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Model independence of $(\infty,2)$-categorical nerves

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arxiv 2206.00660 v1 pith:I5H3RE5A submitted 2022-06-01 math.AT math.CT

Lyne Moser , Viktoriya Ozornova , Martina Rovelli This is my paper · ORCID
classification math.ATmath.CT
keywords inftycategoriescategorynerveembeddingsmodelbeencategorical
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abstract

For most models of $(\infty,2)$-categories an embedding of the $\infty$-category of 2-categories into that of $(\infty,2)$-categories has been constructed in the form of a nerve construction of some flavor. We prove that all those nerve embeddings induce equivalent functors, modulo change of model. We also show that all the nerve embeddings realize the $\infty$-category of 2-categories as the sub-$\infty$-category of $(\infty,2)$-categories that are local with respect to a certain class of maps.

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