# Slightly trivial extensions of a fusion category

## TL;DR

This paper introduces the concept of slightly trivial extensions of fusion categories, exploring their properties and providing examples from rank 3 fusion categories, thus advancing understanding of fusion category extensions.

## Contribution

It defines and studies slightly trivial extensions of fusion categories, offering initial insights and concrete examples from rank 3 categories.

## Key findings

- Defined slightly trivial extensions of fusion categories.
- Provided two explicit examples from rank 3 categories.
- Laid groundwork for further exploration of fusion category extensions.

## Abstract

We introduce and study the notion of slightly trivial extensions of a fusion category which can be viewed as the first level of complexity of extensions. We also provide two examples of slightly trivial extensions which arise from rank $3$ fusion categories.