A new model of dg-categories
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910309280645120 |
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| author | Bermejo, Elena Dimitriadis |
| author_facet | Bermejo, Elena Dimitriadis |
| contents | In this article, we develop a new model for the category of dg-categories. Following Rezk's example in the case of classic Segal spaces, we define dg-Segal spaces: functors between free dg-categories of finite type and simplicial spaces to which we add certain properties. We define also complete dg-Segal spaces, and make their relationship to classic Segal spaces explicit. With the help of two new hypercover constructions, and up to a certain hypothesis, we prove that there exists an equivalence between the homotopy category of dg-categories and the homotopy category of functors defined above with a model structure making the complete dg-Segal spaces into its fibrant objects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_06417 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A new model of dg-categories Bermejo, Elena Dimitriadis Category Theory Algebraic Geometry K-Theory and Homology 18G35, 18A22, 18N40, 18N50, 18N60 In this article, we develop a new model for the category of dg-categories. Following Rezk's example in the case of classic Segal spaces, we define dg-Segal spaces: functors between free dg-categories of finite type and simplicial spaces to which we add certain properties. We define also complete dg-Segal spaces, and make their relationship to classic Segal spaces explicit. With the help of two new hypercover constructions, and up to a certain hypothesis, we prove that there exists an equivalence between the homotopy category of dg-categories and the homotopy category of functors defined above with a model structure making the complete dg-Segal spaces into its fibrant objects. |
| title | A new model of dg-categories |
| topic | Category Theory Algebraic Geometry K-Theory and Homology 18G35, 18A22, 18N40, 18N50, 18N60 |
| url | https://arxiv.org/abs/2308.06417 |