nLab stability under pullback

Contents

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

Last revised on February 26, 2018 at 15:26:16. See the history of this page for a list of all contributions to it.