2020/11/30 by He, Zhenggang
#18A05 #18E10 #18G20 #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2011.14552
This paper mainly studies the relative Gorenstein objects in the extriangulated category C=(C,𝔼,\mathfraks) with a proper class ξ and the related properties of these objects. In the first part, we define the notion of the ξ-Gprojective resolution, and study the relation between ξ-projective resolution and ξ-Gprojective resolution for any object A in C, i.e. A has a C(-,P(ξ))-exact ξ-projective resolution if and only if A has a C(-,P(ξ))-exact ξ-Gprojective resolution. In the second part, we define a particular ξ-Gorenstein projective object in C which called ξ-n-strongly Gprojective object. On this basis, we study the relation between ξ-m-strongly Gprojective object and ξ-n-strongly Gprojective object whenever m≠ n, and give some equivalent characterizations of ξ-n-strongly Gprojective objects. What is more, we give some nice propsitions of ξ-n-strongly Gprojective objects.