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| Main Author: | |
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| Format: | Preprint |
| Published: |
2016
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1609.00566 |
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| _version_ | 1866914261435940864 |
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| author | Ornaghi, Mattia |
| author_facet | Ornaghi, Mattia |
| contents | The aim of this paper is to prove that the A$_{\infty}$-nerve of two quasi-equivalent A$_{\infty}$-categories (linear over a commutative ring) are weak-equivalent in the Joyal model structure. As a consequence we prove that the A$_{\infty}$-nerve of a pretriangulated A$_{\infty}$-category is a stable $\infty$-category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1609_00566 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Some properties of the A$_{\infty}$-nerve Ornaghi, Mattia Algebraic Geometry Category Theory 18G70, 18N50, 18N60 The aim of this paper is to prove that the A$_{\infty}$-nerve of two quasi-equivalent A$_{\infty}$-categories (linear over a commutative ring) are weak-equivalent in the Joyal model structure. As a consequence we prove that the A$_{\infty}$-nerve of a pretriangulated A$_{\infty}$-category is a stable $\infty$-category. |
| title | Some properties of the A$_{\infty}$-nerve |
| topic | Algebraic Geometry Category Theory 18G70, 18N50, 18N60 |
| url | https://arxiv.org/abs/1609.00566 |