nLab tetracategory

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Contents

Context

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

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

Weak 4-categories

The structure of a tetracategories was given by Todd Trimble.

A polished writeup of the definition appears in section 3.2 of

Strict 4-categories

On strict 4-categories

via a string diagram-calculus:

  • Manuel Araújo: String diagrams for 4-categories and fibrations of mapping 4-groupoids, Theory and Applications of Categories 41 38 (2024) 1352-1398 [arXiv:2012.03797, tac:41-38]

Last revised on September 26, 2024 at 11:19:50. See the history of this page for a list of all contributions to it.