nLab
monoidal fibration

Contents

Context

Monoidal categories

monoidal categories

With symmetry

With duals for objects

With duals for morphisms

With traces

Closed structure

Special sorts of products

Semisimplicity

Morphisms

Internal monoids

Examples

Theorems

In higher category theory

Contents

Definition

A monoidal fibration is a functor Φ:EB\Phi\colon E\to B such that

If BB is cartesian monoidal, then monoidal fibrations over BB are equivalent to pseudofunctors B opMonCatB^{op} \to MonCat, which are called indexed monoidal categories. In this case the tensor product on EE 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.