A Survey of Definitions of n-Category

TL;DR

This survey reviews ten different definitions of weak n-categories, providing detailed explanations and special cases for low dimensions, serving as a comprehensive reference for researchers in higher category theory.

Contribution

It compiles and compares ten distinct definitions of weak n-categories, clarifying their differences and similarities, and discusses low-dimensional cases in detail.

Findings

Ten definitions of weak n-category presented

Detailed analysis of low-dimensional cases (n=0,1,2)

Provides a comprehensive bibliography

Abstract

Many people have proposed definitions of `weak n-category'. Ten of them are presented here. Each definition is given in two pages, with a further two pages on what happens when n = 0, 1, or 2. The definitions can be read independently. Chatty bibliography follows.