WW-Gorenstein objects in triangulated categories

Abstract

We fix a proper class of triangles ξ in a triangulated category C . Let W be a class of objects in C such that ξxti ξ (W, W′ ) = 0 for all W, W′ ∈ W and all i ≥ 1. In this paper, we introduce the notion of W -Gorenstein objects and G(W) -(co)resolution dimensions of any object in C and study the properties of W -Gorenstein objects and characterize the finite G(W) -(co)resolution dimensions of any object. Some applications are given.