On the straightening of every functor
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917003762073600 |
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| author | Blom, Thomas |
| author_facet | Blom, Thomas |
| contents | We show that any functor between $\infty$-categories can be straightened. More precisely, we show that for any $\infty$-category $\mathcal{C}$, there is an equivalence between the $\infty$-category $(\mathrm{Cat}_{\infty})_{/\mathcal{C}}$ of $\infty$-categories over $\mathcal{C}$ and the $\infty$-category of unital lax functors from $\mathcal{C}$ to the double $\infty$-category $\mathrm{Corr}$ of correspondences. The proof relies on a certain universal property of the Morita category which is of independent interest. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_16539 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the straightening of every functor Blom, Thomas Category Theory Algebraic Topology We show that any functor between $\infty$-categories can be straightened. More precisely, we show that for any $\infty$-category $\mathcal{C}$, there is an equivalence between the $\infty$-category $(\mathrm{Cat}_{\infty})_{/\mathcal{C}}$ of $\infty$-categories over $\mathcal{C}$ and the $\infty$-category of unital lax functors from $\mathcal{C}$ to the double $\infty$-category $\mathrm{Corr}$ of correspondences. The proof relies on a certain universal property of the Morita category which is of independent interest. |
| title | On the straightening of every functor |
| topic | Category Theory Algebraic Topology |
| url | https://arxiv.org/abs/2408.16539 |