A survey of models for $(\infty, n)$-categories

TL;DR

This survey reviews various models for $( abla, n)$-categories, focusing on diagrammatic approaches with sets and simplicial sets, especially for low dimensions, and discusses generalization methods for all $n$.

Contribution

It provides a comprehensive overview of models for $( abla, n)$-categories, highlighting diagram-based approaches and generalization techniques.

Findings

Several models for $( abla, n)$-categories are described.

Focus on models using diagrams of sets and simplicial sets.

Methods for extending models to all $n$ are summarized.

Abstract

We give describe several models for $(\infty,n)$-categories, with an emphasis on models given by diagrams of sets and simplicial sets. We look most closely at the cases when $n \leq 2$, then summarize methods of generalizing for all $n$.