Templicial nerve of an A-infinity category
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917852126117888 |
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| author | Marques, Violeta Borges Mertens, Arne |
| author_facet | Marques, Violeta Borges Mertens, Arne |
| contents | The framework of templicial vector spaces was put forth in arXiv:2302.02484v2 as a suitable generalization of simplicial sets in order to develop a theory of enriched quasi-categories, called quasi-categories in vector spaces. We construct a lift of Faonte's $A_{\infty}$-nerve arXiv:1312.2127v2 which lands in templicial vector spaces. Further, we show that when restricted to dg-categories, this nerve recovers the templicial dg-nerve of arXiv:2005.04778v4, and that the nerve of any $A_{\infty}$-category is a quasi-category in vector spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19751 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Templicial nerve of an A-infinity category Marques, Violeta Borges Mertens, Arne Category Theory Algebraic Topology 18G70, 18N60 (Primary) The framework of templicial vector spaces was put forth in arXiv:2302.02484v2 as a suitable generalization of simplicial sets in order to develop a theory of enriched quasi-categories, called quasi-categories in vector spaces. We construct a lift of Faonte's $A_{\infty}$-nerve arXiv:1312.2127v2 which lands in templicial vector spaces. Further, we show that when restricted to dg-categories, this nerve recovers the templicial dg-nerve of arXiv:2005.04778v4, and that the nerve of any $A_{\infty}$-category is a quasi-category in vector spaces. |
| title | Templicial nerve of an A-infinity category |
| topic | Category Theory Algebraic Topology 18G70, 18N60 (Primary) |
| url | https://arxiv.org/abs/2411.19751 |