Costability of Comodules
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914959425798144 |
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| author | Chen, Fei Yu |
| author_facet | Chen, Fei Yu |
| contents | Given a ring $R$, we have a classical result stating that the ordinary category of modules is the abelianization of the category of augmented $R$-algebras. Analogously, using the framework of infinity categories and higher algebra, Francis showed that the infinity category of $R$-modules is the stabilization of the infinity category of augmented $R$-algebras. In this work we show a dual result for coalgebras over a cooperad $Q$: namely that given a coalgebra $C$, comodules over $C$ are the costabilization of coalgebras over $C$, which is the universal stable category with a finite colimit preserving functor to coalgebras over $C$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08082 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Costability of Comodules Chen, Fei Yu Category Theory Algebraic Topology Rings and Algebras 18N70 Given a ring $R$, we have a classical result stating that the ordinary category of modules is the abelianization of the category of augmented $R$-algebras. Analogously, using the framework of infinity categories and higher algebra, Francis showed that the infinity category of $R$-modules is the stabilization of the infinity category of augmented $R$-algebras. In this work we show a dual result for coalgebras over a cooperad $Q$: namely that given a coalgebra $C$, comodules over $C$ are the costabilization of coalgebras over $C$, which is the universal stable category with a finite colimit preserving functor to coalgebras over $C$. |
| title | Costability of Comodules |
| topic | Category Theory Algebraic Topology Rings and Algebras 18N70 |
| url | https://arxiv.org/abs/2404.08082 |