$k$-linear Morita theory
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910720110624768 |
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| author | Doni, Matteo |
| author_facet | Doni, Matteo |
| contents | In this paper, we prove the standard comparison used by mathematicians between the idempotent complete pretriangulated dg-categories, over a unitary and commutative ring $k$, and the idempotent complete $k$-linear stable $\infty$-categories. Our approach is completely included in the $\infty$-categorical theory. To achieve the target we will reinterpret the Morita theory for dg-categories and we set the Morita theory for $k$-linear stable $\infty$-category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15895 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $k$-linear Morita theory Doni, Matteo Category Theory Commutative Algebra Algebraic Geometry Algebraic Topology 18G80 (Primary), 18G35: 18N40 (Secondary):14A20:55U35 In this paper, we prove the standard comparison used by mathematicians between the idempotent complete pretriangulated dg-categories, over a unitary and commutative ring $k$, and the idempotent complete $k$-linear stable $\infty$-categories. Our approach is completely included in the $\infty$-categorical theory. To achieve the target we will reinterpret the Morita theory for dg-categories and we set the Morita theory for $k$-linear stable $\infty$-category. |
| title | $k$-linear Morita theory |
| topic | Category Theory Commutative Algebra Algebraic Geometry Algebraic Topology 18G80 (Primary), 18G35: 18N40 (Secondary):14A20:55U35 |
| url | https://arxiv.org/abs/2406.15895 |