Extriangulated categories were introduced by Nakaoka and Palu by extracting the similarities between exact categories and triangulated categories. A notion of homotopy cartesian square in an extriangulated category is defined in this article. We prove that in an extriangulated category with enough projective objects, the extension subcategory of two covariantly finite subcategories is covariantly finite. As an application, we give a simultaneous generalization of a result of X. W. Chen (2009) and...
Cryo-electron microscopy (Cryo-EM) is a powerful technique to produce 3-dimensional density maps for large molecular complexes. Although many atomic structures have been solved from cryo-EM density maps, it is challenging to derive atomic structures when the resolution of density maps is not sufficiently high. Geometrical shape representation of secondary structural components in a medium-resolution density map enhances modeling of atomic structures.We compare two methods in producing surface representation...
Zhou and Zhu have shown that if is an -angulated category and is a cluster tilting subcategory of , then the quotient category is an -abelian category. We show that if has Auslander-Reiten -angles, then has Auslander-Reiten -exact sequences.
For an integer , we introduce a simultaneous generalization of -exact categories and -angulated categories, referred to as one-sided -suspended categories. Notably, one-sided -angulated categories are specific instances of this structure. We establish a framework for transitioning from these generalized categories to their -angulated counterparts. Additionally, we present a method for constructing -angulated quotient categories from Frobenius -prile categories. Our results unify and extend...
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.
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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