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arXiv · 1811.03798

The equivalence of two discretenesses of triangulated categories

Lingling Yao·Dong Yang
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Abstract

Given an ST-triple $(\mathcal{C},\mathcal{D},M)$ one can associate a co-$t$-structure on $\mathcal{C}$ and a $t$-structure on $\mathcal{D}$. It is shown that the discreteness of $\mathcal{C}$ with respect to the co-$t$-structure is equivalent to the discreteness of $\mathcal{D}$ with respect to the $t$-structure. As a special case, the discreteness of $\mathcal{D}^b(\mathrm{mod} A)$ in the sense of Vossieck is equivalent to the discreteness of $K^b(\mathrm{proj} A)$ in a dual sense, where $A$ is a finite-dimensional algebra.

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BibTeXRIS

Lingling Yao, Dong Yang. 2018-11-09. The equivalence of two discretenesses of triangulated categories. https://arxiv.org/abs/1811.03798

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