# What is an equivalence in a higher category?

## TL;DR

This survey provides a unified overview of the concept of equivalence across strict and higher categories, including $(n)$ and $(
)$-categories, emphasizing their interrelations.

## Contribution

It systematically consolidates the notion of equivalence in higher categories, offering a clear, uniform framework for understanding these complex relationships.

## Key findings

- Unified framework for equivalences in strict and higher categories
- Clarification of equivalence notions in $(n)$ and $(
)$-categories
- Enhanced understanding of categorical relationships in higher dimensions

## Abstract

The purpose of this survey is to present in a uniform way the notion of equivalence between strict $n$-categories or $(\infty,n)$-categories, and inside a strict $(n+1)$-category or $(\infty,n+1)$-category.