A model structure on the category of A$_\infty$-categories with strict morphisms
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913917091971072 |
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| author | Ornaghi, Mattia |
| author_facet | Ornaghi, Mattia |
| contents | We prove that the category of (strictly unital) A$_\infty$-categories, linear over a commutative ring $R$, with strict A$_\infty$-morphisms has a cofibrantly generated model structure. In this model structure every object is fibrant and the cofibrant objects have cofibrant morphisms. As a consequence we prove that the semi-free A$_\infty$-categories (resp. resolutions) are cofibrant objects (resp. resolution) in this model structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22847 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A model structure on the category of A$_\infty$-categories with strict morphisms Ornaghi, Mattia Category Theory Algebraic Geometry Algebraic Topology 14F08, 18G70, 18N40 We prove that the category of (strictly unital) A$_\infty$-categories, linear over a commutative ring $R$, with strict A$_\infty$-morphisms has a cofibrantly generated model structure. In this model structure every object is fibrant and the cofibrant objects have cofibrant morphisms. As a consequence we prove that the semi-free A$_\infty$-categories (resp. resolutions) are cofibrant objects (resp. resolution) in this model structure. |
| title | A model structure on the category of A$_\infty$-categories with strict morphisms |
| topic | Category Theory Algebraic Geometry Algebraic Topology 14F08, 18G70, 18N40 |
| url | https://arxiv.org/abs/2506.22847 |