# nLab cobase change

limits and colimits

# Contents

## Definition

Cobase change is another term for pushout of a morphism:

if

$\begin{array}{ccc}X& \to & U\\ ↓& & ↓\\ Y& \to & Y{\bigsqcup }_{X}U\end{array}$\array{ X &\to & U \\ \downarrow && \downarrow \\ Y &\to& Y \sqcup_X U }

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

## Remarks

Revised on May 19, 2010 09:09:08 by Urs Schreiber (131.211.232.167)