Geodesic
A higher Whitehead theorem and the embedding of quasicategories in prederivators
Homology, homotopy, and applications, Tome 22 (2020) no. 1, pp. 117-139.

Voir la notice de l'article provenant de la source International Press of Boston

We prove a categorified Whitehead theorem showing that the $2$-functor $\mathrm{HO}$ associating a prederivator to a quasicategory reflects equivalences. The question of whether $\mathrm{HO}$is bicategorically fully faithful (that is, whether morphisms and $2$-morphisms can be uniquely lifted from prederivators to quasicategories) is more subtle.We can show that small quasicategories embed fully faithfully, both bicategorically and with respect to a certain simplicial enrichment, into prederivators defined on arbitrary small categories. When the quasicategories are not necessarily small, or when the prederivators are defined only on homotopically finite categories, the $2$-categorical argument breaks down, although the simplicial version continues to go through. We give a conjectural counterexample to bicategorical full faithfulness in general.
DOI : 10.4310/HHA.2020.v22.n1.a8
Classification : 18G55, 55U35
Keywords: prederivator, quasicategory, models for higher categories 
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     title = {A higher {Whitehead} theorem and the embedding of quasicategories in prederivators},
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     pages = {117--139},
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Kevin Arlin. A higher Whitehead theorem and the embedding of quasicategories in prederivators. Homology, homotopy, and applications, Tome 22 (2020) no. 1, pp. 117-139. doi : 10.4310/HHA.2020.v22.n1.a8. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2020.v22.n1.a8/

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