On the $\infty$categorical Whitehead theorem and the embedding of quasicategories in prederivators
Abstract
We show that small quasicategories embed, both simplicially and 2categorically, 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2016
 arXiv:
 arXiv:1612.06980
 Bibcode:
 2016arXiv161206980A
 Keywords:

 Mathematics  Category Theory;
 Mathematics  Algebraic Topology
 EPrint:
 19 pages