On bifibrations of model categories
Résumé
In this article, we develop a notion of Quillen bifibration which combines the two notions of Grothendieck bifibration and of Quillen model structure. In particular, given a bifibration p : E → B, we describe when a family of model structures on the fibers E A and on the basis category B combines into a model structure on the total category E, such that the functor p preserves cofibrations, fibrations and weak equivalences. Using this Grothendieck construction for model structures, we revisit the traditional definition of Reedy model structures, and possible generalizations, and exhibit their bifibrational nature.
Domaines
Logique en informatique [cs.LO] Informatique et langage [cs.CL] Algèbres quantiques [math.QA] Géométrie algébrique [math.AG] Informatique et théorie des jeux [cs.GT] Logiciel mathématique [cs.MS] Théorie et langage formel [cs.FL] Langage de programmation [cs.PL] Catégories et ensembles [math.CT] Logique [math.LO] Topologie algébrique [math.AT]
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