For any abelian category A, the length-2 part of the derived category admits a natural 2-category of extensions that the triangulated structure alone cannot see, and the enhancement formalism of arXiv:2409.17489 reproduces it.
Kaledin, How to glue derived categories , Bull
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On 2-categories of extensions
For any abelian category A, the length-2 part of the derived category admits a natural 2-category of extensions that the triangulated structure alone cannot see, and the enhancement formalism of arXiv:2409.17489 reproduces it.