Definable functoriality of tensor-triangular spectra

2025/11/13 by Bird, Isaac, Williamson, Jordan
#18E45 #18F99 #18G80 #Algebraic Topology (math.AT) #Category Theory (math.CT) #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2511.10454

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.

Citations

• Homological stratification and descent
• Definable functors between triangulated categories
• On surjectivity in tensor triangular geometry
• The homological spectrum via definable subcategories
• Cosupport in tensor triangular geometry
• The spectrum of prime ideals in tensor triangulated categories
• Isomorphisms between left and right adjoints

Related

• The tensor triangular geometry of fully faithful functors
• Functors on triangulated tensor categories
• On surjectivity in tensor triangular geometry
• On functoriality and the tensor product property in noncommutative tensor-triangular geometry
• Tensor triangular geometry of modules over the mod 2 Steenrod algebra