Invertible exterior powers

2025/07/20 by Kevin Coulembier, Coulembier, Kevin
Mathematics · #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2507.14803

openalex publication_date 2025/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a proof of the fact that in a symmetric monoidal category over a field of characteristic zero, objects with an invertible exterior power are rigid. As an application we prove two recent conjectures on dimensions in symmetric monoidal categories by Baez, Moeller and Trimble and further conjectures by Baez and Trimble.

Citations

• Tannaka Reconstruction and the Monoid of Matrices
• Finite symmetric algebras in tensor categories and Verlinde categories of algebraic groups
• 2-Rig Extensions and the Splitting Principle
• Incompressible tensor categories
• Uniqueness of fiber functors and universal Tannakian categories
• Invariants of the special orthogonal group and an enhanced Brauer category
• Tensor categorical foundations of algebraic geometry

Related

• Locally rigid ∞-categories
• Duality in Monoidal Categories
• Rigid Algebras and Cospans
• Symmetries of a rigid braided category
• Finite symmetric algebras in tensor categories and Verlinde categories of algebraic groups