nLab monoidal relative category

Context

Monoidal categories

monoidal categories

With braiding

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

(,1)(\infty,1)-Categories

Contents

Idea

A model for monoidal (∞,1)-categories.

Definition

A monoidal relative category is a monoidal category equipped with a relative category structure such that the monoidal product preserves weak equivalences.

Properties

The canonical functor from the quasicategorical localization of the relative category of monoidal relative categories, monoidal relative functors, and monoidal Dwyer–Kan equivalences to the quasicategory of monoidal quasicategories is a weak equivalence.

References

Last revised on May 1, 2025 at 05:08:34. See the history of this page for a list of all contributions to it.