The theory of associative $n$-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 $n$-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.
Christoph Dorn, Associative $n$-categories, talk at 103rd Peripatetic Seminar on Sheaves and Logic (pdf).
Christoph Dorn, Associative $n$-categories, PhD thesis (pdf arXiv:1812.10586).
David Reutter and Jamie Vicary, High-level techniques for homotopy construction in associative $n$-categories (arXiv:1902.03831).
Last revised on March 26, 2019 at 18:30:28. See the history of this page for a list of all contributions to it.