The spectrum of the singularity category of a category algebra

TL;DR

This paper computes the spectrum of the singularity category of a finite projective EI category algebra, providing insights into its tensor triangulated structure.

Contribution

It explicitly determines the spectrum of the singularity category for finite projective EI category algebras, a novel computation in this context.

Findings

Spectrum of the singularity category is explicitly computed.

Provides a description of the tensor triangulated structure.

Advances understanding of category algebra singularities.

Abstract

Let $\C$ be a finite projective EI category and $k$ be a field. The singularity category of the category algebra $k\C$ is a tensor triangulated category. We compute its spectrum in the sense of Balmer.