In previous work, based on the work of Zwara and Yoshino, we defined and studied degenerations of objects in triangulated categories analogous to the degeneration of modules. In triangulated categories ${\mathcal{T}}$, it is surprising that the zero object may degenerate. We show that the triangulated subcategory of ${\mathcal{T}}$ generated by the objects that are degenerations of zero coincides with the triangulated subcategory of ${\mathcal{T}}$ consisting of the objects with a vanishing image in the Grothendieck group $K_{0}({\mathcal{T}})$ of ${\mathcal{T}}$.

中文翻译：

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在三角分类中退化 0

在之前的工作中，基于 Zwara 和 Yoshino 的工作，我们定义和研究了类似于模块退化的三角类别中的对象退化。在三角分类中${\mathcal{T}}$，令人惊讶的是零对象可能会退化。我们证明了三角化的子类别${\mathcal{T}}$由零退化的对象生成的三角子类别与${\mathcal{T}}$由格洛腾迪克组中具有消失图像的对象组成$K_{0}({\mathcal{T}})$的${\mathcal{T}}$.