Rouquier's cocovering

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

Revised on November 3, 2009 15:40:22 by Vi V? (