# Tensor-triangular rigidity in chromatic homotopy theory

## TL;DR

This paper investigates conditions ensuring the uniqueness of enhancements in tensor-triangulated categories, applying these results to chromatic homotopy theory to establish new uniqueness results.

## Contribution

It introduces conditions for the interaction of enhancements with categorical decompositions and applies them to chromatic homotopy theory.

## Key findings

- Established new criteria for enhancement uniqueness in tensor-triangulated categories.
- Proved the uniqueness of enhancements in specific chromatic homotopy contexts.
- Provided a framework connecting categorical decompositions with enhancement properties.

## Abstract

We study the uniqueness of enhancements of tensor-triangulated categories. To do so, we provide conditions under which these enhancements interact well with categorical decompositions. As an application we obtain new results about the uniqueness of enhancements in chromatic homotopy theory.