A k-linear triangulated category without a model

TL;DR

This paper presents a specific example of a k-linear triangulated category over a field of characteristic zero that lacks a DG-enhancement, highlighting limitations in existing models.

Contribution

It provides the first known example of a k-linear triangulated category without a DG-enhancement, expanding understanding of the structure of such categories.

Findings

First example of a k-linear triangulated category without a DG-enhancement

Shows limitations of existing models for triangulated categories

Highlights differences from previous non-linear examples

Abstract

In this paper we give an example of a triangulated category, linear over a field of characteristic zero, which does not carry a DG-enhancement. The only previous examples of triangulated categories without a model have been constructed by Muro, Schwede and Strickland. These examples are however not linear over a field.