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

Revised on August 20, 2017 01:55:55 by Mike Shulman (76.167.222.204)