Corpus ID: 119685361

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

@article{Arlin2016OnT,
  title={On the \$\infty\$-categorical Whitehead theorem and the embedding of quasicategories in prederivators.},
  author={Kevin Arlin},
  journal={arXiv: Category Theory},
  year={2016}
}
  • Kevin Arlin
  • Published 2016
  • Mathematics
  • arXiv: Category Theory
  • 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… CONTINUE READING
    A model structure on prederivators for $(\infty,1)$-categories
    1
    Higher homotopy categories, higher derivators, and K-theory
    1

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