[[Fibre bundle]]
# Category of fibre bundles

Let $\cat C$ be a [[subcategory]] of [[Category of topological spaces]] and $X$ be a space in $\cat C$.
The **category of fibre bundles over $X$**, denoted $\cat{Bund}^{\cat C}_X$,[^1] is a [[category]] where
an object is a [[fibre bundle]]
and a morphism is a [[bundle map]]. #m/def/topology  

## Relates

- A subcategory with richer structure is [[Category of vector bundles]]

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#state/develop | #lang/en | #SemBr

[^1]: If $\cat C$ is clear from context we instead denote the category by $\cat{Bund}_{X}$.