(see also *Chern-Weil theory*, parameterized homotopy theory)

A *sub-bundle* is a subobject in a category of bundles.

If $\left[ E \overset{fb}{\to} X\right]$ is a bundle, then a sub-bundle is a monomorphism

$S \hookrightarrow E$

in the given slice category over $X$, hence

$\array{
S && \hookrightarrow && E
\\
& {}_{\mathllap{\exists!}}\searrow && \swarrow_{\mathrlap{fb}}
\\
&& X
}$

- Given a real vector bundle with orthogonal structure, then the sub-bundle whose fibers are the unit spheres is called the unit sphere bundle of the vector bundle.

Created on October 23, 2017 at 09:05:27. See the history of this page for a list of all contributions to it.