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arXiv · 1612.06980

On the $\infty$-categorical Whitehead theorem and the embedding of quasicategories in prederivators

Kevin Arlin
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Abstract

We show that small quasicategories embed, both simplicially and 2-categorically, into prederivators defined on arbitrary small categories, so that in some senses prederivators can serve as a model for $(\infty,1)$-categories. The result for quasicategories that are not necessarily small, or analogously for small quasicategories when mapped to prederivators defined only on finite categories, is not as strong. We prove, instead, a Whitehead theorem that prederivators (defined on any domain) detect equivalences between arbitrarily large quasicategories.

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Kevin Arlin. 2016-12-21. On the $\infty$-categorical Whitehead theorem and the embedding of quasicategories in prederivators. https://doi.org/10.4310/hha.2020.v22.n1.a8

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