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M. Herschend, Y. Liu, H. Nakaoka introduced -exangulated categories, which are a simultaneous generalization of -exact categories and -angulated categories. This paper consists of two results on -exangulated categories: (1) we give an equivalent characterization of axiom (EA2); (2) we provide a new way to construct a closed subfunctor of an -exangulated category.
Let and be abelian categories with enough projective and injective objects, and a left exact additive functor. Then one has a comma category . It is shown that if is -exact, then is a (hereditary) cotorsion pair in and ) is a (hereditary) cotorsion pair in if and only if is a (hereditary) cotorsion pair in and and are closed under extensions. Furthermore, we characterize when special preenveloping classes in abelian categories and can induce special preenveloping classes...
The aim of this article is to study the relative Auslander bijection in -exangulated categories. More precisely, we introduce the notion of generalized Auslander-Reiten-Serre duality and exploit a bijection triangle, which involves the generalized Auslander-Reiten-Serre duality and the restricted Auslander bijection relative to the subfunctor. As an application, this result generalizes the work by Zhao in extriangulated categories.
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