长度范畴的宽子范畴与砖块有限性
Wide subcategories and brick-finiteness for length categories
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中文总结 AI 辅助
该研究将有限维代数砖块有限性特征推广到有限秩阿贝尔长度范畴，证明范畴砖块有限的条件，基于交换关系给出证明，还作为推论扩展了第一个砖块布劳尔 - 索尔猜想的有效性。
中文摘要 AI 辅助
我们将有限维代数已知的砖块有限性的一个特征推广到有限秩的阿贝尔长度范畴。我们证明，这样一个范畴是砖块有限的，当且仅当每个挠类由一个宽子范畴生成，且每个无挠类由一个宽子范畴余生成。证明基于跨宽区间的砖块标签的交换关系，这是单心集突变的一种体现。作为推论，我们将第一个砖块布劳尔 - 索尔猜想的有效性扩展到这种情形。
英文摘要
We extend to abelian length categories of finite rank a characterisation of brick-finiteness known for finite-dimensional algebras. We prove that such a category is brick-finite if and only if every torsion class is generated by a wide subcategory and every torsionfree class is cogenerated by a wide subcategory. The proof is based on an exchange relation for brick labels across wide intervals which is a shadow of the mutation of simple minded collections. As a corollary,we extend the validity of the first Brick Brauer-Thrall conjecture to this setting.
