# nLab n-functor

Higher functors

### Context

#### Higher category theory

higher category theory

# Higher functors

## Idea

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

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

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