4 citations · 7 across the 9 of their papers we have counts for
5 papers · 1 filter
Definable functoriality of tensor-triangular spectra
Isaac Bird, Jordan Williamson
We prove that the homological and Balmer spectra in tensor-triangular geometry are functorial in certain definable functors, thereby providing an alternative perspective on functor…
The shift-homological spectrum and parametrising kernels of rank functions
Isaac Bird, Jordan Williamson, Alexandra Zvonareva
For any compactly generated triangulated category we introduce two topological spaces, the shift-spectrum and the shift-homological spectrum. We use them to parametrise a family of…
Definable functors between triangulated categories
Isaac Bird, Jordan Williamson
We systematically develop the theory of definable functors between compactly generated triangulated categories. Such functors preserve pure triangles, pure injective objects, and d…
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…
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…