Definable functors between triangulated categories with applications to tensor-triangular geometry and representation theory
I Bird, J Williamson - arXiv preprint arXiv:2310.02159, 2023 - arxiv.org
We systematically develop, study, and give applications of definable functors between
compactly generated triangulated categories. Such functors preserve pure triangles, pure …
compactly generated triangulated categories. Such functors preserve pure triangles, pure …
The homological spectrum via definable subcategories
I Bird, J Williamson - arXiv preprint arXiv:2304.05179, 2023 - arxiv.org
We develop an alternative approach to the homological spectrum through the lens of
definable subcategories. This culminates in a proof that the homological spectrum is …
definable subcategories. This culminates in a proof that the homological spectrum is …
The index with respect to a contravariantly finite subcategory
F Fedele, P Jorgensen, A Shah - arXiv preprint arXiv:2401.09291, 2024 - arxiv.org
The index in triangulated categories plays a key role in the categorification of cluster
algebras; specifically, it categorifies the notion of $ g $-vectors. For an object $ C $ in a …
algebras; specifically, it categorifies the notion of $ g $-vectors. For an object $ C $ in a …