∞-Tilting Subcategories in Extriangulated Categories

Zhen Zhang , Jiaqun Wei , Shance Wang

Chinese Annals of Mathematics, Series B ›› 2024, Vol. 45 ›› Issue (1) : 151 -160.

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Chinese Annals of Mathematics, Series B ›› 2024, Vol. 45 ›› Issue (1) : 151 -160. DOI: 10.1007/s11401-024-0008-6
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∞-Tilting Subcategories in Extriangulated Categories

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Abstract

In this paper, the authors introduce a new definition of ∞-tilting (resp. cotilting) subcategories with infinite projective dimensions (resp. injective dimensions) in an extriangulated category. They give a Bazzoni characterization of ∞-tilting (resp. cotilting) subcategories. Also, they obtain a partial Auslander-Reiten correspondence between ∞-tilting (resp. cotilting) subcategories and coresolving (resp. resolving) subcategories with an $\mathbb{E}$-projective generator (resp. $\mathbb{E}$-injective cogenerator) in an extriangulated category.

Keywords

Extriangulated category / ∞-Tilting subcategory / Auslander-Reiten correspondence / Bazzoni characterization

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Zhen Zhang,Jiaqun Wei,Shance Wang. ∞-Tilting Subcategories in Extriangulated Categories. Chinese Annals of Mathematics, Series B, 2024, 45(1): 151-160 DOI:10.1007/s11401-024-0008-6

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