# nLab stability under pullback

### Context

#### Limits and colimits

limits and colimits

# Contents

## Idea

There are several contexts in which it is of relevance that a certain property of a morphism $f : A \to B$ is preserved (or stable) under pullback, i.e. also shared by the the morphism $\tilde{f}: X \times_B A \to X$ for any pullback diagram

$\array{ X \times_B A &\to& A \\ _{\tilde{f}}\downarrow && \downarrow_f \\ X &\to& B } \,.$

Geometers prefer to say “stable under base change”.

## Examples

Revised on September 9, 2011 01:51:13 by Mike Shulman (71.136.238.9)