nLab
Grothendieck construction for model categories

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 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

Idea

The Grothendieck construction may be lifted from categories to model categories, where is is (or should) serve as a presentation for the (infinity,1)-Grothendieck construction.

References

The first model category version of the Grothendieck construction was given in

This article (Roig 94) had a mistake, which was fixed in

  • Alexandru E. Stanculescu, Bifibrations and weak factorisation systems, Applied Categorical Structures 20.1, p.19–30, (2012) (doi:10.1007/s10485-009-9214-3)

The construction was then generalized in

For the special case of pseudofunctors with values in groupoids, a model category version of the Grothendieck construction was discussed in

Created on March 17, 2018 at 07:32:32. See the history of this page for a list of all contributions to it.