A monoidal Dold-Kan correspondence for comodules
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866914742516318208 |
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| author | Péroux, Maximilien |
| author_facet | Péroux, Maximilien |
| contents | We provide examples of inductive fibrant replacements in fibrantly generated model categories constructed as Postnikov towers. These provide new types of arguments to compute homotopy limits in model categories. We provide examples for simplicial and differential graded comodules. Our main application is to show that simplicial comodules and connective differential graded comodules are Quillen equivalent and their derived cotensor products correspond. We deduce that the rational $A$-theory of a simply connected space $X$ is equivalent to the $K$-theory of perfect chain complexes with a $C_*(X; \mathbb{Q})$-comodule structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_04835 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A monoidal Dold-Kan correspondence for comodules Péroux, Maximilien Algebraic Topology Category Theory 16T15, 18N40, 18G31, 18G35, 55U15 We provide examples of inductive fibrant replacements in fibrantly generated model categories constructed as Postnikov towers. These provide new types of arguments to compute homotopy limits in model categories. We provide examples for simplicial and differential graded comodules. Our main application is to show that simplicial comodules and connective differential graded comodules are Quillen equivalent and their derived cotensor products correspond. We deduce that the rational $A$-theory of a simply connected space $X$ is equivalent to the $K$-theory of perfect chain complexes with a $C_*(X; \mathbb{Q})$-comodule structure. |
| title | A monoidal Dold-Kan correspondence for comodules |
| topic | Algebraic Topology Category Theory 16T15, 18N40, 18G31, 18G35, 55U15 |
| url | https://arxiv.org/abs/2108.04835 |