Definable functoriality of tensor-triangular spectra
Category Theory
2026-03-18 v2 Commutative Algebra
Algebraic Topology
Representation Theory
Abstract
We prove that the homological and Balmer spectra in tensor-triangular geometry are functorial in certain definable functors, thereby providing an alternative perspective on functoriality in tensor-triangular geometry from the viewpoint of purity, and generalising current results in the literature.
Cite
@article{arxiv.2511.10454,
title = {Definable functoriality of tensor-triangular spectra},
author = {Isaac Bird and Jordan Williamson},
journal= {arXiv preprint arXiv:2511.10454},
year = {2026}
}
Comments
v1: 11pp. The results are an improved and generalised version of results that appeared in the original version of arXiv:2310.02159. v2: minor changes. Version accepted in Pacific J. Math