Invertible exterior powers

TL;DR

This paper proves that objects with invertible exterior powers in symmetric monoidal categories over characteristic zero fields are rigid, and applies this to confirm several conjectures on dimensions in such categories.

Contribution

It establishes a key property linking invertible exterior powers to rigidity and verifies multiple conjectures in the field.

Findings

Objects with invertible exterior powers are rigid in symmetric monoidal categories.

Confirmed conjectures on dimensions by Baez, Moeller, and Trimble.

Extended understanding of structural properties in symmetric monoidal categories.

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.