nLab dg-category presented by a dg-model category

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Context

Model category theory

model category, model ∞ \infty -category

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

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

Model structures

for ∞\infty-groupoids

for ∞-groupoids

for equivariant ∞\infty-groupoids

for rational ∞\infty-groupoids

for rational equivariant ∞\infty-groupoids

for nn-groupoids

for ∞\infty-groups

for ∞\infty-algebras

general ∞\infty-algebras

specific ∞\infty-algebras

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

Idea

Any dg-model category MM presents an associated dg-category, whose objects are the cofibrant fibrant objects of MM, and whose mapping complexes are given by the dg-enrichment of MM. 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.

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