Definable functoriality of tensor-triangular spectra

Isaac Bird and Jordan Williamson

Vol. 341 (2026), No. 1, 33–44

DOI: 10.2140/pjm.2026.341.33

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.

Keywords

tensor triangular geometry, homological spectrum, definable functor, definable category, purity

Mathematical Subject Classification

Primary: 18G80, 18F99, 18E45

Milestones

Received: 4 August 2025

Revised: 13 January 2026

Accepted: 13 January 2026

Published: 10 March 2026