$\infty$-Dold-Kan correspondence via representation theory
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912517459017728 |
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| author | Sava, Chiara |
| author_facet | Sava, Chiara |
| contents | We give a purely derivator-theoretical reformulation and proof of a classic result of Happel and Ladkani, showing that it occurs uniformly across stable derivators and it is then independent of coefficients. The resulting equivalence provides a bridge between homotopy theory and representation theory: indeed, our result is a derivator-theoretic version of the $\infty$-Dold-Kan correspondence for bounded chain complexes. Moreover, our equivalence can also be realized as an action of a spectral bimodule in the setting of universal tilting theory developed by Groth and Šťovíček. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_00762 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | $\infty$-Dold-Kan correspondence via representation theory Sava, Chiara Representation Theory Algebraic Topology Category Theory 55U35 (Primary), 16G20, 16E35, 18G80 (Secondary) We give a purely derivator-theoretical reformulation and proof of a classic result of Happel and Ladkani, showing that it occurs uniformly across stable derivators and it is then independent of coefficients. The resulting equivalence provides a bridge between homotopy theory and representation theory: indeed, our result is a derivator-theoretic version of the $\infty$-Dold-Kan correspondence for bounded chain complexes. Moreover, our equivalence can also be realized as an action of a spectral bimodule in the setting of universal tilting theory developed by Groth and Šťovíček. |
| title | $\infty$-Dold-Kan correspondence via representation theory |
| topic | Representation Theory Algebraic Topology Category Theory 55U35 (Primary), 16G20, 16E35, 18G80 (Secondary) |
| url | https://arxiv.org/abs/2211.00762 |