nLab Rouquier's cocovering

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 $\{S_1,\ldots, S_k\}$ 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