Cofinality Theorems of Infinity Categories and Algebraic K-Theory
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914785778466816 |
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| author | Matsukawa, Hisato |
| author_facet | Matsukawa, Hisato |
| contents | In this paper, we establish a theorem that proves a condition when an inclusion morphism between simplicial sets becomes a weak homotopy equivalence. Additionally, we present two applications of this result. The first application demonstrates that cofinal full inclusion functors of (\infty)-categories are weak homotopy equivalences. For our second application, we provide an alternative proof of Barwick's cofinality theorem of algebraic (K)-theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03498 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cofinality Theorems of Infinity Categories and Algebraic K-Theory Matsukawa, Hisato Algebraic Topology K-Theory and Homology 18F25 In this paper, we establish a theorem that proves a condition when an inclusion morphism between simplicial sets becomes a weak homotopy equivalence. Additionally, we present two applications of this result. The first application demonstrates that cofinal full inclusion functors of (\infty)-categories are weak homotopy equivalences. For our second application, we provide an alternative proof of Barwick's cofinality theorem of algebraic (K)-theory. |
| title | Cofinality Theorems of Infinity Categories and Algebraic K-Theory |
| topic | Algebraic Topology K-Theory and Homology 18F25 |
| url | https://arxiv.org/abs/2405.03498 |