On 2-categories of extensions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910964136280064 |
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| author | Kaledin, D. |
| author_facet | Kaledin, D. |
| contents | This is essentially an illustration for the general technology of homotopical enhancements developed recently in arxiv:2409.17489. We take the derived category of an abelian category, and we look at the full subcategory spanned by complexes of length 2. This has a natural refinement to a 2-category that we call "the 2-category of extensions". However, just using the triangulated structure on the derived category is not enough to obtain this refinement. In this short note, we first construct the 2-category of extensions by hand -- that is, using abelian category techniques -- and then show how it can be recovered very easily and naturally in the enhanced formalism of arxiv:2409.17489. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17286 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On 2-categories of extensions Kaledin, D. Algebraic Geometry Category Theory K-Theory and Homology This is essentially an illustration for the general technology of homotopical enhancements developed recently in arxiv:2409.17489. We take the derived category of an abelian category, and we look at the full subcategory spanned by complexes of length 2. This has a natural refinement to a 2-category that we call "the 2-category of extensions". However, just using the triangulated structure on the derived category is not enough to obtain this refinement. In this short note, we first construct the 2-category of extensions by hand -- that is, using abelian category techniques -- and then show how it can be recovered very easily and naturally in the enhanced formalism of arxiv:2409.17489. |
| title | On 2-categories of extensions |
| topic | Algebraic Geometry Category Theory K-Theory and Homology |
| url | https://arxiv.org/abs/2505.17286 |