A Survey of Definitions of n-Category
Tom Leinster

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.
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Taxonomy
TopicsEducational Technology and Assessment · Image Retrieval and Classification Techniques · Geological Modeling and Analysis
