∞-Tilting Subcategories in Extriangulated Categories

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