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arXiv · 2412.07455

Realization functors in algebraic triangulated categories

Janina C. Letz·Julia Sauter
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Abstract

Let $\mathcal{T}$ be an algebraic triangulated category and $\mathcal{C}$ an extension-closed subcategory with $\operatorname{Hom}(\mathcal{C}, \Sigma^{<0} \mathcal{C})=0$. Then $\mathcal{C}$ has an exact structure induced from exact triangles in $\mathcal{T}$. Keller and Vossieck say that there exists a triangle functor $\operatorname{D}^b(\mathcal{C}) \to \mathcal{T}$ extending the inclusion $\mathcal{C} \subseteq \mathcal{T}$. We provide the missing details for a complete proof.

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Janina C. Letz, Julia Sauter. 2024-12-10. Realization functors in algebraic triangulated categories. https://arxiv.org/abs/2412.07455

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