nLab vertical composition

Contents

Context

2-Category theory

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

Contents

Definition

In a 2-category (and more generally in higher category theory) 2-morphisms have a composition along the 1-morphisms that they go between.

x y . \array{ & \nearrow &\Downarrow& \searrow \\ x &&\to&& y \\ & \searrow &\Downarrow& \nearrow } \,.

This is in contrast to the other composition operation, along objects, which is called horizontal composition.

Examples

References

For the notion of vertical composition of natural transformations (ie. composition in functor categories):

Last revised on August 18, 2023 at 15:18:15. See the history of this page for a list of all contributions to it.