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math.CT2023★ 1 cited
The homological spectrum via definable subcategories
Isaac Bird, Jordan Williamson
We develop an alternative approach to the homological spectrum of a tensor-triangulated category through the lens of definable subcategories. This culminates in a proof that the ho…
math.CT2022★ 4 cited
Duality pairs, phantom maps, and definability in triangulated categories
Isaac Bird, Jordan Williamson
We define duality triples and duality pairs in compactly generated triangulated categories and investigate their properties. This enables us to give an elementary way to determine…
math.CT2020
Lifting (co)stratifications between tensor triangulated categories
Liran Shaul, Jordan Williamson
We give necessary and sufficient conditions for stratification and costratification to descend along a coproduct preserving, tensor-exact -linear functor between -linear tens…