Auslander-Buchweitz Context and Co-t-structures
Auslander-Buchweitz Context and Co-t-structures
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DOI：
10.1007/s10485-011-9271-2
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发表时间：
2010-02
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通讯作者：
O. M. Hernández;Edith Corina Sáenz Valadez;Valente Santiago Vargas;M. J. S. Salorio
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作者：
O. M. Hernández;Edith Corina Sáenz Valadez;Valente Santiago Vargas;M. J. S. Salorio
我们证明了三角范畴上的相对 Auslander-Buchweitz 上下文与某些三角子范畴上的 co-t 结构的概念一致（见定理 3.8）。在 Krull-Schmidt 案例中，我们在 co-t 结构和共悬、预覆盖子类别之间建立了双射对应关系（参见定理 3.11）。我们还根据相对同调代数给出了有界 co-t 结构的表征。还研究了淤积等级和共t结构之间的关系。我们证明，淤积类 ω 在包含 ω 的最小厚三角子类别上产生有界非退化 co-t 结构。我们还给出了有界 co-t 结构的描述（参见定理 5.10）。最后，作为有界派生范畴的特殊情况的应用，其中阿贝尔遗传范畴是 Hom 有限、Ext 有限且具有倾斜对象（参见 Happel 和 Reiten，Math Z 232:559–588, 1999），我们给出有限淤积生成元集 ω=add(ω) 和有界 co-t 结构之间的双射对应关系（参见定理 6.7）。
We show that the relative Auslander–Buchweitz context on a triangulated categorycoincides with the notion of co-t-structure on certain triangulated subcategory of(see Theorem 3.8). In the Krull–Schmidt case, we establish a bijective correspondence between co-t-structures and cosuspended, precovering subcategories (see Theorem 3.11). We also give a characterization of bounded co-t-structures in terms of relative homological algebra. The relationship between silting classes and co-t-structures is also studied. We prove that a silting classωinduces a bounded non-degenerated co-t-structure on the smallest thick triangulated subcategory ofcontainingω. We also give a description of the bounded co-t-structures on(see Theorem 5.10). Finally, as an application to the particular case of the bounded derived categorywhereis an abelian hereditary category which is Hom-finite, Ext-finite and has a tilting object (see Happel and Reiten, Math Z 232:559–588, 1999), we give a bijective correspondence between finite silting generator setsω=add(ω) and bounded co-t-structures (see Theorem 6.7).