# nLab horizontal composition

### Context

#### 2-Category theory

2-category theory

## Structures on 2-categories

#### Higher category theory

higher category theory

# Contents

## Definition

In a 2-category, the composition of 2-morphisms along objects is called horizontal composition .

This is in contrast to the vertical composition of 2-morphisms, which is their composition along 1-morphisms.

## Properties

Horizontal and vertical composition are subject to the compatibility condition called the interchange law.

## Examples

Revised on September 30, 2011 16:21:34 by Tim Porter (193.48.130.2)