تقرير
Support $\tau$-tilting subcategories in exact categories
| العنوان: | Support $\tau$-tilting subcategories in exact categories |
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| المؤلفون: | Pan, Jixing, Zhang, Yaohua, Zhu, Bin |
| المصدر: | J. Alg. 636(15): 455-482, 2023 |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Representation Theory, 16G10, 18E40, 16S90, 18E99 |
| الوصف: | Let $\mathcal{E}=(\mathcal{A},\mathcal{S})$ be an exact category with enough projectives $\mathcal{P}$. We introduce the notion of support $\tau$-tilting subcategories of $\mathcal{E}$. It is compatible with existing definitions of support $\tau$-tilting modules (subcategories) in various context. It is also a generalization of tilting subcategories of exact categories. We show that there is a bijection between support $\tau$-tilting subcategories and certain $\tau$-cotorsion pairs. Given a support $\tau$-tilting subcategory $\mathcal{T}$, we find a subcategory $\mathcal{E}_{\mathcal{T}}$ of $\mathcal{E}$ which is an exact category and $\mathcal{T}$ is a tilting subcategory of $\mathcal{E}_{\mathcal{T}}$. If $\mathcal{E}$ is Krull-Schmidt, we prove the cardinal $|\mathcal{T}|$ is equal to the number of isomorphism classes of indecomposable projectives $Q$ such that ${\rm Hom}_{\mathcal{E}}(Q,\mathcal{T})\neq 0$. We also show a functorial version of Brenner-Butler's theorem. Comment: 20 pages. There are some modifications in the published version on J. Alg |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1016/j.jalgebra.2023.08.031 |
| URL الوصول: | http://arxiv.org/abs/2301.10437 |
| رقم الأكسشن: | edsarx.2301.10437 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1016/j.jalgebra.2023.08.031 |
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