4 papers
Duality in tensor-triangular geometry via proxy-smallness
Thomas Peirce, Jordan Williamson
We make a systematic study of duality phenomena in tensor-triangular geometry, generalising and complementing previous results of Balmer--Dell'Ambrogio--Sanders and Dwyer--Greenlee…
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…