Symmetric and exterior powers of categories

TL;DR

This paper introduces the concepts of symmetric and exterior powers of categories, integrating them into categorified Koszul complexes, and explores their impact on categorical characters in matrix 2-representations.

Contribution

It presents new definitions for symmetric and exterior powers of categories and analyzes their effects on categorical characters, advancing the theory of categorified algebraic structures.

Findings

Defined symmetric and exterior powers of categories

Analyzed effects on categorical characters of matrix 2-representations

Provided examples illustrating these power operations

Abstract

We define symmetric and exterior powers of categories, fitting into categorified Koszul complexes. We discuss examples and calculate the effect of these power operations on the categorical characters of matrix 2-representations.