Let $T$ be a triangulated category. A triangulated subcategory $S$ of $T$ closed under small products is Bousfield if the inclusion $S\hookrightarrow T$ has a right adjoint. Two Bousfield subcategories ${S}_{1},{S}_{2}$ of are said to intersect properly if for any objects ${I}_{1}\in {S}_{1}$, ${I}_{2}\in {S}_{2}$ every morphism ${I}_{1}\to {I}_{2}$ or ${I}_{2}\to {I}_{1}$ factors through an object in the subcategory ${S}_{1}\cap {S}_{2}$. A finite family of Bousfield subcategories $\{{S}_{1},\dots ,{S}_{k}\}$ of $T$ which pairwise intersect properly is a Rouquier’s cocovering if in addition ${\cap}_{i=1}^{k}{S}_{i}=0$.
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