nLab
opposite model structure

Contents

Context

Model category theory

Definition
Related concepts
References

Definition

If a category $C$ carries a model category structure, then the opposite category $C^{op}$ carries the opposite model structure:

its weak equivalences are those morphisms whose dual was a weak equivalence in $C$ , its fibrations are those morphisms that were cofibrations in $C$ and its cofibrations are those that were fibrations in $C$ .

Related concepts

slice model structure

References

Philip Hirschhorn, Proposition 7.1.10 of: Model Categories and Their Localizations, AMS Math. Survey and Monographs Vol 99 (2002) (ISBN:978-0-8218-4917-0, pdf toc, pdf)

Last revised on August 29, 2020 at 10:16:11. See the history of this page for a list of all contributions to it.

nLab
opposite model structure

Context

Model category theory

Definitions

Morphisms

Universal constructions

Producing new model structures

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

Model structures

for $\infty$ -groupoids

for rational $\infty$ -groupoids

for $n$ -groupoids

for $\infty$ -groups

for $\infty$ -algebras

general

specific

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

Contents

Definition

Definition

Related concepts

References

nLab opposite model structure

Context

Model category theory

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

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

Model structures

for ∞\infty-groupoids

for rational ∞\infty-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

Contents

Definition

Definition

Related concepts

References

nLab
opposite model structure

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

for $\infty$ -groupoids

for rational $\infty$ -groupoids

for $n$ -groupoids

for $\infty$ -groups

for $\infty$ -algebras

for $(\infty,1)$ -categories

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

for $(\infty,1)$ -operads

for $(n,r)$ -categories

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