Let be a triangulated category. A triangulated subcategory of closed under small products is Bousfield if the inclusion has a right adjoint. Two Bousfield subcategories of are said to intersect properly if for any objects , every morphism or factors through an object in the subcategory . A finite family of Bousfield subcategories of which pairwise intersect properly is a Rouquier’s cocovering if in addition .
Raphael Rouquier, Dimensions of triangulated categories, J. K-Theory 1 (2008), no. 2, 193–256.
Daniel Murfet, Rouquier’s cocovering theorem and well-generated triangulated categories, arxiv:0904.2685