Definitions
Transfors between 2-categories
Morphisms in 2-categories
Structures in 2-categories
Limits in 2-categories
Structures on 2-categories
2-morphism
A 2-morphism in an n-category is a k-morphism for : it is a higher morphism between ordinary 1-morphisms.
So in the hierarchy of -categories, the first step where 2-morphisms appear is in a 2-category. This includes cases such as bicategory, 2-groupoid or double category.
There are different geometric shapes for higher structures: globes, simplices, cubes, etc. Accordingly, 2-morphisms may appear in different guises:
A globular -morphism looks like this:
A simplicial -morphism looks like this:
A cubical -morphism looks like this:
Of course, using identity morphisms and composition, we can turn one into the other; which is more fundamental depends on which shapes you prefer.
In the 2-category Cat, 2-morphisms are natural transformations between functors.
In a path 2-groupoid 2-morphisms are certain surfaces or images of surfaces in a space, going between paths in that space.
Last revised on November 2, 2022 at 09:20:04. See the history of this page for a list of all contributions to it.