A subcategory $\mathscr{W}$ of an abelian category is called wide if it is closed under kernels, cokernels, and extensions. Wide subcategories are of interest in representation theory because of their links to other homological and combinatorial objects, established among others by Ingalls-Thomas and Marks-Sťovicek. If $d \geqslant 1$ is an integer, then Jasso introduced the notion of $d$-abelian categories, where kernels, cokernels, and extensions have been replaced by longer complexes. Wide subcategories can be generalised to this situation. Important examples of $d$-abelian categories arise as the $d$-cluster tilting subcategories $\mathscr{M}_{n,d}$ of $\operatorname{mod} A_n^{d-1}$, where $A_n^{d-1}$ is a higher Auslander algebra of type $A$ in the sense of Iyama. This paper gives a combinatorial description of the wide subcategories of $\mathscr{M}_{n,d}$ in terms of what we call non-interlacing collections.

中文翻译：

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A 类较高 Auslander 代数的较高宽子类别的分类

阿贝尔范畴的子范畴 $\mathscr{W}$ 如果在内核、内核和扩展下是封闭的，则称为宽。广泛的子类别在表示论中很受关注，因为它们与其他同调和组合对象相关联，这些对象由 Ingalls-Thomas 和 Marks-Sťovicek 建立。如果 $d \geqslant 1$ 是一个整数，那么 Jasso 引入了 $d$-abelian 类别的概念，其中内核、cokernels 和扩展已被更长的复合体取代。广泛的子类别可以推广到这种情况。$d$-abelian 类别的重要例子是 $d$-cluster 倾斜子类别 $\mathscr{M}_{n,d}$ 的 $\operatorname{mod} A_n^{d-1}$，其中 $ A_n^{d-1}$ 是 Iyama 意义上的 $A$ 类型的更高 Auslander 代数。