# nLab monoidal fibration

### Context

#### Monoidal categories

monoidal categories

# Contents

## Definition

A monoidal fibration is a functor $\Phi\colon E\to B$ such that

If $B$ is cartesian monoidal, then monoidal fibrations over $B$ are equivalent to pseudofunctors $B^{op} \to MonCat$, which are called indexed monoidal categories. In this case the tensor product on $E$ is the external tensor product of the indexed monoidal category.

## References

Last revised on August 20, 2017 at 01:55:55. See the history of this page for a list of all contributions to it.