Deformation Theory for $(\infty,n)$-categories
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913804517900288 |
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| author | Kositsyn, Roman |
| author_facet | Kositsyn, Roman |
| contents | For an $(\infty,n)$-category $\mathscr E$ we define an $(\infty,1)$ category $\mathrm{TwAr}(\mathscr E)$ and provide an isomorphism between the stabilization of the overcategory of $\mathscr E$ in $\mathrm{Cat}_{(\infty,n)}$ and the $\infty$-category of spectrum-valued functors on $\mathrm{TwAr}(\mathscr E)$. We use this to develop the deformation theory of $(\infty,n)$-categories and apply it to given an $\infty$-categorical characterization of lax-idempotent monads. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16326 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deformation Theory for $(\infty,n)$-categories Kositsyn, Roman Category Theory 18N65 (Primary) 18N60, 18N15 (Secondary) For an $(\infty,n)$-category $\mathscr E$ we define an $(\infty,1)$ category $\mathrm{TwAr}(\mathscr E)$ and provide an isomorphism between the stabilization of the overcategory of $\mathscr E$ in $\mathrm{Cat}_{(\infty,n)}$ and the $\infty$-category of spectrum-valued functors on $\mathrm{TwAr}(\mathscr E)$. We use this to develop the deformation theory of $(\infty,n)$-categories and apply it to given an $\infty$-categorical characterization of lax-idempotent monads. |
| title | Deformation Theory for $(\infty,n)$-categories |
| topic | Category Theory 18N65 (Primary) 18N60, 18N15 (Secondary) |
| url | https://arxiv.org/abs/2504.16326 |