On 2-categories of extensions

D. Kaledin

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arXiv · 2505.17286

On 2-categories of extensions

D. Kaledin

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Abstract

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.

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D. Kaledin. 2025-05-22. On 2-categories of extensions. https://arxiv.org/abs/2505.17286

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