On the $\infty$-categorical Whitehead theorem and the embedding of quasicategories in prederivators
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2016
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| _version_ | 1866915232203407360 |
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| author | Arlin, Kevin |
| author_facet | Arlin, Kevin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1612_06980 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | On the $\infty$-categorical Whitehead theorem and the embedding of quasicategories in prederivators Arlin, Kevin Category Theory Algebraic Topology 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. |
| title | On the $\infty$-categorical Whitehead theorem and the embedding of quasicategories in prederivators |
| topic | Category Theory Algebraic Topology |
| url | https://arxiv.org/abs/1612.06980 |