# nLab dg-category presented by a dg-model category

### Context

#### Model category theory

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

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

Model structures

for $\infty$-groupoids

for ∞-groupoids

for equivariant $\infty$-groupoids

for rational $\infty$-groupoids

for rational equivariant $\infty$-groupoids

for $n$-groupoids

for $\infty$-groups

for $\infty$-algebras

general $\infty$-algebras

specific $\infty$-algebras

for stable/spectrum objects

for $(\infty,1)$-categories

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

for $(\infty,1)$-operads

for $(n,r)$-categories

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

#### Enriched category theory

enriched category theory

## Idea

Any dg-model category $M$ presents an associated dg-category, whose objects are the cofibrant fibrant objects of $M$, and whose mapping complexes are given by the dg-enrichment of $M$. This dg-category has the property of being fibrant in the Dwyer-Kan model structure on dg-categories.

This is the analogue of the simplicially enriched category presented by a simplicial model category.

## Definition

Created on January 6, 2015 at 22:46:21. See the history of this page for a list of all contributions to it.