New examples of non-unique enhancements for triangulated categories

TL;DR

This paper introduces a general method for constructing triangulated categories with multiple, non-unique enhancements, demonstrating that the presence of a t-structure does not guarantee uniqueness of enhancements.

Contribution

It provides new examples of triangulated categories with distinct enhancements, including some with t-structures, challenging previous assumptions about enhancement uniqueness.

Findings

Existence of triangulated categories with non-unique enhancements

Presence of t-structures does not imply enhancement uniqueness

Examples can be linear over a field and have non-degenerate t-structures

Abstract

We present a general procedure for constructing triangulated categories, linear over a field, with distinct enhancements. Some of our examples can be equipped with a (non-degenerate) t-structure, thereby showing that the existence of a t-structure does not imply uniqueness of enhancements, whether in the strong or weak sense (depending on the example).