A semiorthogonal decomposition of a triangulated category is an ordered collection of full triangulated subcategories that generate the category and have no morphisms from a later subcategory to an earlier one, including after shifts. Objects can be reconstructed by successive distinguished triangles with components in the indicated subcategories. Orthogonality in the opposite direction is not required.
For a smooth cubic fourfold, the decomposition
 |
is generated by its Kuznetsov component and the three indicated exceptional line bundles. Here each line bundle denotes the triangulated subcategory it generates.
