[[Vector bundle]]
# Category of vector bundles

The **category of vector bundles over $X$**, denoted $\Vect^{\cat C}_X$,[^1] is a [[category]] where
an object is a [[vector bundle]] over $X$
and a morphism is a [[vector bundle morphism]]. #m/def/topology 

## Closed monoidal structure

#todo

## Related

- There is a forgetful inclusion into [[Category of fibre bundles]].

#
---
#state/tidy | #lang/en | #SemBr

[^1]: If $\cat C$ is clear from context we instead denote the category by $\Vect_X$. There should be no risk of confusing this with ordinary [[Category of vector spaces]].