Relative cluster tilting subcategories in an extriangulated category

Zhang, Zhen; Wang, Shance

doi:10.3934/era.2023083

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“…Recall from [19,Def. 3.1] that a subcategory Y ⊆ C is said to be weak (n + 2)cluster tilting whenever Y = Y ⊥ ≤n+1 = ⊥ ≤n+1 Y.…”

Section: (Nmentioning

confidence: 99%

Extension-closed subcategories in extriangulated categories

Tan¹,

Zhao²

2022

MATH

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<abstract><p>In this paper, we mainly focus on extension-closed subcategories of extriangulated categories. Let $ {\mathcal{X}} $ be an extension-closed subcategory. We show that if $ C $ is $ {\mathcal{X}} $-projective and there is a minimal right almost split deflation in $ {\mathcal{X}} $ ending by $ C $, then there is an $ {\mathfrak{s}} $-triangle ending by $ C $ which is very similar to an Auslander-Reiten triangle in $ {\mathcal{X}} $. We also show that if the extriangulated category admits a negative first extension $ {\mathbb{E}}^{-1} $, and $ {\mathcal{X}} $ is self-orthogonal with respect to $ {\mathbb{E}}^{-1} $, then $ {\mathcal{X}} $ has an exact structure.</p></abstract>

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“…Recall from [19,Def. 3.1] that a subcategory Y ⊆ C is said to be weak (n + 2)cluster tilting whenever Y = Y ⊥ ≤n+1 = ⊥ ≤n+1 Y.…”

Section: (Nmentioning

confidence: 99%