2025/01/13 by He, Zhenggang
#18E05 #18G05 #18G20 #18G25 #Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2501.07140
Let (C,𝔼,\mathfraks) be an extriangulated category with a proper class ξ of 𝔼-triangles. In this paper, we study the quasi-Gorensteinness of extriangulated categories. More precisely, we introduce the notion of quasi-ξ-projective and quasi-ξ-Gorenstein projective objects, investigate some of their properties and their behavior with respect to 𝔼-triangles. Moreover, we give some equivalent characterizations of objects with finite quasi-ξ-Gorenstein projective dimension. As an application, our main results generalize Mashhad and Mohammadi's work in module categories.