nLab
stability under pullback

Contents

Idea

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

X× BA A f˜ f X B. \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)