A bijection triangle in extriangulated categories

Auslander-Reiten-Serre duality for n-exangulated categories

“…Serre duality is a special type of Auslander-Reiten-Serre duality. Krause, Chen-Le and Zhao-Tan-Huang give an equivalent condition for the existence of Serre duality for triangulated, abelian, extriangulated categories, respectively, see [7,21,29]. Our second main result unify and extend their results.…”

“…Dually, one can prove other statements. when C is a triangulated category, it is just Theorem 4.2 in [21], when C is an extriangulated category, it is just Theorem 3.5 in [29].…”

“…δ be a distinguished n-exangle. Then for any X ∈ C, we have the following two commutative diagrams (more details can see [29])…”

Resolution Dimension Relative to Resolving Subcategories in Extriangulated Categories

“…In [12], Nakaoka and Palu introduced the notion of extriangulated categories as a simultaneous generalization of exact categories and extension-closed subcategories of triangulated categories. After that, the study of extriangulated categories has become an active topic, and up to now, many results on exact categories and triangulated categories can be unified in the same framework, e.g., see [8,[12][13][14][15][16]. Recently, Hu, Zhang, Zhou [13] studied a relative homological algebra in an extriangulated category (C , E, s) which parallels the relative homological algebra in triangulated categories and exact categories.…”