Central Support for Triangulated Categories.

For any essentially small triangulated category, the centre of its lattice of thick subcategories is introduced; it is a spatial frame and yields a notion of central support. A relative version of this centre recovers the support theory for tensor triangulated categories and provides a universal notion of cohomological support. Along the way, we establish Mayer–Vietoris sequences for pairs of commuting subcategories. [ABSTRACT FROM AUTHOR]