nLab
associative n-category

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

The theory of associative nn-categories (ANCs) is a model of higher category theory with strictly associative composition, developed by Christoph Dorn, Christopher Douglas and Jamie Vicary. The theory is weakly unital, but has a canonical strictly-unital subtheory to which it can easily be restricted. Despite these strictness properties, it is conjectured that every weak n-category is weakly equivalent to an associative nn-category with strict units.

All the weak structure of an ANC lives in a notion of homotopy between composites. This is similar to the case of a Gray category, which is strictly associative and unital, but which has weak interchangers. In this sense, ANCs can be seen as a generalization of Gray categories.

This theory forms the basis for homotopy.io, a proof assistant for higher category theory which is currently under development.

References

Last revised on March 26, 2019 at 18:30:28. See the history of this page for a list of all contributions to it.