nLab Rouquier's cocovering

Let TT be a triangulated category. A triangulated subcategory SS of TT closed under small products is Bousfield if the inclusion STS\hookrightarrow T has a right adjoint. Two Bousfield subcategories S 1,S 2S_1, S_2 of are said to intersect properly if for any objects I 1S 1I_1\in S_1, I 2S 2I_2\in S_2 every morphism I 1I 2I_1\to I_2 or I 2I 1I_2\to I_1 factors through an object in the subcategory S 1S 2S_1\cap S_2. A finite family of Bousfield subcategories {S 1,,S k}\{S_1,\ldots, S_k\} of TT which pairwise intersect properly is a Rouquier’s cocovering if in addition i=1 kS i=0\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

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