发表机构
School of Mathematics and Statistics, Changsha University of Science and Technology（长沙理工大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明外三角范畴的典范理想商中，子范畴的更高正交性可由典范悬垂或环的幂零性刻画，并给出对象级识别准则，将截断转化为识别更高正交性的精确判据。
AI 中文摘要
外三角范畴的典范理想商自然具有单侧三角或预三角结构。一个基本问题是，这些商结构是否仍保留足够信息以恢复被分解子范畴的更高正交性。我们证明，对于强函子有限 $n$-刚性子范畴，此类信息由典范悬垂（canonical suspension）的幂零性编码，且等价地由典范环（canonical loop）的幂零性编码。更精确地说，该幂零性刻画了双侧极大 $n$-正交性。我们进一步建立了一个对象层面的识别准则，该准则将单侧更高正交性与第 $n$ 次悬垂或环的消失相结合。在三角化情形中，我们的结果给出了已知截断构造的逆命题，并表明商是 $n$-截断的当且仅当子范畴是 $(n+1)$-丛倾斜的。此外，在非分裂情形下，幂零指数恰好为 $n$。这些结果将截断从更高正交性的一个推论转变为识别它的一个精确准则。
英文摘要
Canonical ideal quotients of extriangulated categories admit natural one-sided triangulated or pretriangulated structures. A fundamental question is whether these quotient structures still retain enough information to recover higher orthogonality properties of the subcategory being factored out. We show that, for a strongly functorially finite $n$-rigid subcategory, such information is encoded by the nilpotency of the canonical suspension and, equivalently, of the canonical loop. More precisely, this nilpotency characterizes two-sided maximal $n$-orthogonality. We further establish an objectwise recognition criterion that combines one-sided higher orthogonality with the vanishing of the $n$th suspension or loop. In the triangulated setting, our results give a converse to the known truncation construction and show that the quotient is $n$-truncated if and only if the subcategory is $(n+1)$-cluster tilting. Moreover, in the nonsplit case, the nilpotency index is exactly $n$. These results turn truncation from a consequence of higher orthogonality into a sharp criterion for recognizing it.
Comments18 pages
