nLab
stability under pullback

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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 &\longrightarrow& A \\ {}^{\mathllap{\tilde{f}}} \big\downarrow && \big\downarrow {}^{\mathrlap{f}} \\ X &\longrightarrow& B } \,.

Geometers prefer to say “stable under base change”.

Examples

Last revised on October 13, 2021 at 04:09:35. See the history of this page for a list of all contributions to it.