The Auslander-Reiten correspondence about ∞-cotilting objects in extriangulated categories

Zhang, Zhen and Wang, Shance (2024) The Auslander-Reiten correspondence about ∞-cotilting objects in extriangulated categories. Miskolc Mathematical Notes, 25 (2). pp. 1025-1036. ISSN 1787-2413

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Abstract

In this paper, we introduce ∞-cotilting objects in an extriangulated category. The definition given unifies those of Wakamatsu cotilting modules and of cotilting objects in an extriangulated category. We give a similar Bazzoni characterization and a partial Auslander-Reiten correspondence between ∞-cotilting objects and resolving subcategories in an extriangulated category, which recovers several different results from the literature. More importantly, extensions of the known results for Wakamatsu cotilting modules and for cotilting objects are very natural, but nontrivial, and we use a new method to prove them. At the same time, we give a dual version respect to the ∞-tilting objects.

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