# Simple current auto-equivalences of modular tensor categories

## TL;DR

This paper explores how invertible objects can be used to construct auto-equivalences in modular tensor categories, establishing conditions for their monoidal, braided, or pivotal properties and demonstrating their application on real-world examples.

## Contribution

It introduces a systematic method for constructing auto-equivalences from invertible objects and analyzes their properties within modular tensor categories.

## Key findings

- Derived conditions for auto-equivalences to be monoidal, braided, or pivotal.
- Constructed explicit auto-equivalences for several real-world modular tensor categories.
- Analyzed the composition of auto-equivalences built from invertible objects.

## Abstract

In this short note we investigate the process of constructing auto-equivalences of modular tensor categories using invertible objects. We derive conditions on the invertible object for the resulting auto-equivalence to be either monoidal, braided, or pivotal. We also discuss the composition of these auto-equivalences constructed from invertible objects. To demonstrate the practicality of this construction, we construct auto-equivalences of several real-world examples of modular tensor categories.