Spahn
Grothendieck construction in HTT

The Grothendieck construction relates

  • categories of fibrations with contravariant functor categories with codomain CatCat

  • categories of fibrations in groupoids with contravariant functor categories with codomain GrpdGrpd

and dually

  • categories of cofibrations with covariant functor categories with codomain CatCat

  • categories of cofibrations in groupoids with covariant functor categories with codomain GrpdGrpd

To categorify this constructions to (,1)(\infty,1)-category theory we have the following dictionary of notions

On the level of model categories this is accomplished in the following way:

Requisites

enriched model categories

(sSetsSet is an excellent model category Example A.3.2.18)

Proposition 2.1.4.8 (p.65): For a simplicial set SS the ovecategory sSet/SsSet/S is a simplicial enriched model category. A.3.1.7

(co)fibrations

cartesian fibration?

Last revised on June 29, 2012 at 11:55:28. See the history of this page for a list of all contributions to it.