nLab
opposite model structure

Contents

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 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

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

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

References

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