nLab
enriched model category

Context

Model category theory

model category

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

Presentation of (,1)(\infty,1)-categories

Model structures

for \infty-groupoids

for ∞-groupoids

for nn-groupoids

for \infty-groups

for \infty-algebras

general

specific

for stable/spectrum objects

for (,1)(\infty,1)-categories

for stable (,1)(\infty,1)-categories

for (,1)(\infty,1)-operads

for (n,r)(n,r)-categories

for (,1)(\infty,1)-sheaves / \infty-stacks

Enriched category theory

Contents

Idea

An enriched model category is an enriched category CC together with the structure of a model category on the underlying category C 0C_0 such that both structures are compatible in a reasonable way.

Definition

Let VV be a monoidal model category.

A VV-enriched model category is

The last two conditions here are equivalent to the fact that the copower

:C×VC \otimes : C \times V \to C

is a Quillen bifunctor.

Properties

Change of enrichment

(…)

Examples

References

Last revised on July 19, 2018 at 13:26:05. See the history of this page for a list of all contributions to it.