Tensor product of A$_{\infty}$-categories
| Autor: | Ornaghi, Mattia |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Preliminary version, 31 pages. Comments are welcome |
| Databáze: | arXiv |
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