The Homotopy Theory of $A_\infty$Categories
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917208308842496 |
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| author | Ornaghi, Mattia |
| author_facet | Ornaghi, Mattia |
| contents | In this paper we describe the homotopy category of the $A_\infty$categories. To do that we introduce the notion of semi-free $A_\infty$category, which plays the role of standard cofibration. Moreover, we define the non unital $A_\infty$ (resp. DG)categories with cofibrant morphisms and we prove that any non unital $A_\infty$ (resp. DG)category has a resolution of this kind. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05325 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Homotopy Theory of $A_\infty$Categories Ornaghi, Mattia Algebraic Geometry Algebraic Topology Category Theory 14F08, 18E35, 18G70 In this paper we describe the homotopy category of the $A_\infty$categories. To do that we introduce the notion of semi-free $A_\infty$category, which plays the role of standard cofibration. Moreover, we define the non unital $A_\infty$ (resp. DG)categories with cofibrant morphisms and we prove that any non unital $A_\infty$ (resp. DG)category has a resolution of this kind. |
| title | The Homotopy Theory of $A_\infty$Categories |
| topic | Algebraic Geometry Algebraic Topology Category Theory 14F08, 18E35, 18G70 |
| url | https://arxiv.org/abs/2408.05325 |