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Mathematics > Representation Theory
Title: A bijection between support $τ$-tilting subcategories and $τ$-cotorsion pairs in extriangulated categories
(Submitted on 6 Mar 2024 (v1), last revised 23 Apr 2024 (this version, v3))
Abstract: Let $\mathscr{C}$ be an extriangulated category with enough projectives and injectives. We give a new definition of tilting subcategories of $\mathscr{C}$ and prove it coincides with the definition given in [19]. As applications, we introduce the notions of support $\tau$-tilting subcategories and $\tau$-cotorsion pairs of $\mathscr{C}$. We build a bijection between support $\tau$-tilting subcategories and certain $\tau$-cotorsion pairs. Moreover, this bijection induces a bijection between tilting subcategories and certain cotorsion pairs.
Submission history
From: Zhiwei Zhu [view email][v1] Wed, 6 Mar 2024 08:48:07 GMT (11kb)
[v2] Mon, 22 Apr 2024 10:44:44 GMT (11kb)
[v3] Tue, 23 Apr 2024 01:46:58 GMT (11kb)
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