AI 中文总结
本文针对弱逼近三角范畴中的强有界对象范畴，在有限强有限维数条件下，明确了其容许有界t-结构的条件，并证明了该结构的唯一性，为三角化范畴相关问题提供了关键结论。
AI 中文摘要
在弱逼近三角范畴中，强有界对象与整体维数密切相关，且在三角化扩张的唯一性问题中发挥重要作用。本文研究强有界对象的满子范畴何时容许有界t-结构。在称为有限强有限维数的有限性条件下，我们的主要结果表明：该情况恰好发生在该子范畴与环境三角范畴中有界对象的满子范畴一致时；此时，有界t-结构在等价意义下唯一，更进一步，该唯一性在有界对象的满子范畴上无条件成立。
英文摘要
Strongly bounded objects in a weakly approximable triangulated category are known to relate closely to global dimension and to play a significant role in the uniqueness problem for triangulated enhancements. In this paper, we investigate when the full subcategory of strongly bounded objects admits a bounded $t$-structure. Our main result, under a finiteness condition termed the finite strong finitistic dimension, states that this happens exactly when the subcategory agrees with the full subcategory of bounded objects in the ambient triangulated category. In that case, the bounded $t$-structure is unique up to equivalence; even more, the uniqueness holds unconditionally on the full subcategory of bounded objects.
Comments20 pages
