nLab
n-functor

Context

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

Higher functors

Idea

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

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