nLab n-functor

Higher functors


Higher category theory

higher category theory

Basic concepts

Basic theorems





Universal constructions

Extra properties and structure

1-categorical presentations

Higher functors


An nn-functor is simply a functor between nn-categories. Similarly, an \infty-functor is a functor between \infty-categories.

Of course, as the definition of nn-category gets more complicated as nn increases, so does the appropriate definition of functor. This explains why one says ‘nn-functor’ instead of simply ‘functor’ all along. On the other hand, anything that goes between nn-categories, if it deserves to be called anything like ‘functor’ at all, will be an nn-functor, so the prefix is not really necessary.

An nn-natural transformation goes between nn-functors, and there are things to go between those as well, etc. The most general concept is an nn-kk-transfor.

Special cases

Last revised on January 24, 2013 at 22:34:13. See the history of this page for a list of all contributions to it.