nLab
vertical composition

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

Created on September 9, 2010 08:12:37 by Urs Schreiber (77.80.22.58)