# nLab cobase change

### Context

#### Limits and colimits

limits and colimits

# Contents

## Definition

Cobase change is another term for pushout of a morphism:

if

$\array{ X &\to & U \\ \downarrow && \downarrow \\ Y &\to& Y \sqcup_X U }$

is a pushout square in some category then the morphism $U \to U \sqcup_X Y$ is the cobase change or cobase extension of $X \to Y$ along $X \to U$.