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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2411.10300 |
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| _version_ | 1866909993666609152 |
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| author | Ornaghi, Mattia |
| author_facet | Ornaghi, Mattia |
| contents | In this paper we define the tensor product of two A$_{\infty}$-categories and two A$_{\infty}$-functors. This tensor product makes the category of A$_{\infty}$-categories symmetric monoidal (up to homotopy), and the category A$_{\infty}$Cat$^u$/$_{\approx}$ a closed symmetric monoidal category. Moreover, we define the derived tensor product making Ho(A$_{\infty}$Cat), the homotopy category of the A$_{\infty}$-categories, a closed symmetric monoidal category. We provide also an explicit description of the internal homs in terms of A$_{\infty}$- functors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10300 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tensor product of A$_{\infty}$-categories Ornaghi, Mattia Algebraic Geometry Category Theory 14F08, 18E35, 18G70 In this paper we define the tensor product of two A$_{\infty}$-categories and two A$_{\infty}$-functors. This tensor product makes the category of A$_{\infty}$-categories symmetric monoidal (up to homotopy), and the category A$_{\infty}$Cat$^u$/$_{\approx}$ a closed symmetric monoidal category. Moreover, we define the derived tensor product making Ho(A$_{\infty}$Cat), the homotopy category of the A$_{\infty}$-categories, a closed symmetric monoidal category. We provide also an explicit description of the internal homs in terms of A$_{\infty}$- functors. |
| title | Tensor product of A$_{\infty}$-categories |
| topic | Algebraic Geometry Category Theory 14F08, 18E35, 18G70 |
| url | https://arxiv.org/abs/2411.10300 |