n-functor

- homotopy hypothesis-theorem
- delooping hypothesis-theorem
- periodic table
- stabilization hypothesis-theorem
- exactness hypothesis
- holographic principle

- (n,r)-category
- Theta-space
- ∞-category/∞-category
- (∞,n)-category
- (∞,2)-category
- (∞,1)-category
- (∞,0)-category/∞-groupoid
- n-category = (n,n)-category
- 2-category, (2,1)-category
- 1-category
- 0-category
- (?1)-category?
- (?2)-category?

- n-poset = (n-1,n)-category
- n-groupoid = (n,0)-category

- categorification/decategorification
- geometric definition of higher category
- Kan complex
- quasi-category
- simplicial model for weak ∞-categories?

- algebraic definition of higher category
- stable homotopy theory

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.

- implication (a $(-1)$-functor)
- function (a $0$-functor)
- functor (a $1$-functor)
- 2-functor, including pseudo functor
- (∞,1)-functor
- (∞,n)-functor

Revised on January 24, 2013 22:34:13
by Urs Schreiber
(82.113.99.233)