# nLab local trivialization

## Idea

For $p \colon E \to X$ a fiber bundle with typical fiber $F$, then a local trivialization is a cover $U \to X$ such that there is a pullback square of the form

$\array{ U \times F &\longrightarrow& E \\ \downarrow &(pb)& \downarrow^{\mathrlap{p}} \\ U &\longrightarrow& X }$

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