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 \(\mathcal {D}^{b}(\textsf {mod} A)\) in the sense of Vossieck is equivalent to the discreteness of K^b(projA) in a dual sense, where A is a finite-dimensional algebra.

中文翻译：

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三角分类的两个离散概念的等价性

给定一个ST-三重\（（\ mathcal {C}，\ mathcal {d}，M）\）可以助关联吨-结构上（{C} \ \ mathcal）\和吨上-结构\ （\ math {D} \）。结果表明，\（\ mathcal {C} \）相对于co- t结构的离散性等效于\（\ mathcal {D} \）相对于t-结构的离散性。作为一种特殊情况，在Vossieck的意义上\（\ mathcal {D} ^ {b}（\ textsf {mod} A）\）的离散性在对偶意义上等于K ^b（proj A）的离散性，其中A 是有限维代数。