AI 中文总结
基于对0 - Auslander范畴的研究，建立d - Auslander三角化范畴与(d + 2) - 项复形范畴联系，给出代数三角化范畴允许特定理想商的条件，证明d - 簇倾斜子范畴是关键来源，回答了Iyama提出的相关问题。
AI 中文摘要
基于对0 - Auslander范畴的近期研究，我们建立了d - Auslander三角化范畴与同伦意义下的(d + 2) - 项复形范畴之间的联系。给出了一个精确的同调条件，在此条件下一个代数三角化范畴允许一个与\(\mathcal{K}^{[-d - 1,0]}(\mathcal{A})\)等价的三角化理想商。接着证明了三角化范畴中的d - 簇倾斜子范畴是d - Auslander三角化范畴的关键来源。利用这些结构结果，我们回答了Iyama在arXiv:2509.08246附录中提出的一个问题，即当\(\mathcal{N}\)是弱幂等完备代数(d + 4) - 角化范畴时，\(\mathcal{K}^{[-d - 1,0]}(\mathcal{N})\)允许一个三角化结构。
英文摘要
Building on recent studies of 0-Auslander categories, we establish a connection between $d$-Auslander extriangulated categories and categories of $(d+2)$-term complexes up to homotopy. We give a precise homological condition under which an algebraic extriangulated category admits an extriangulated ideal quotient equivalent to $\mathcal{K}^{[-d-1,0]}(\mathcal{A})$. We then demonstrate that $d$-cluster-tilting subcategories in triangulated categories serve as a key source of $d$-Auslander extriangulated categories. Using these structural results, we answer a question posed by Iyama in the Appendix of arXiv:2509.08246 by proving that $\mathcal{K}^{[-d-1,0]}(\mathcal{N})$ admits a triangulated structure when $\mathcal{N}$ is a weakly idempotent complete algebraic $(d+4)$-angulated category.
CommentsClarified several arguments and added references
