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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]

We discuss the notion of strongly unbounded type for abelian length categories; this is closely related to the Second Brauer–Thrall Conjecture for Artin algebras. A new ingredient is the space of characters in the sense of Crawley-Boevey. [ABSTRACT FROM AUTHOR]