strict 2-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
- algebraic definition of higher category
- stable homotopy theory

A *strict 2-functor* is a 2-functor between strict 2-categories which strictly respects the composition operation of 1-morphisms and 2-morphisms. This is in contrast to *weak 2-functors* (also called *pseudofunctors*) which may respect the composition of 1-morphisms only up to natural isomorphism (hence up to 2-morphisms in the 2-category of categories).

While the generally “correct” concepts in 2-category theory are *weak 2-categories* with *weak 2-functors* between them, it is often useful to recognize strict 2-functors among weak 2-functors, or to replace, up to eqivalence of 2-categories and pseudonatural transformation , weak 2-functors by strict ones.

Let Cat be the *1-category* of categories, regarded as a Bénabou cosmos for enriched category theory via its cartesian closed category-structure.

Notice that strict 2-categories may be identified with Cat-enriched categories. Under this identification, strict 2-functors are Cat-enriched functors.

Last revised on July 13, 2018 at 03:56:41. See the history of this page for a list of all contributions to it.