# nLab tetracategory

### Context

#### Higher category theory

higher category theory

# Contents

## Idea

Tetracategories are the algebraic definition of higher category for the most general (i.e. weak) 4-categories.

## Properties

By the discussion at k-tuply monoidal (n,r)-category a tetracategory with a single object may be regarded as the delooping of a monoidal tricategory. This is discussed in (Hoffnung).

## References

The structure of a tetracategories was given by Todd Trimble.

A polished writeup of the definition appears in section 3.2 of

Revised on May 19, 2012 14:09:35 by Urs Schreiber (89.204.155.233)