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Journal Articles Advances in Mathematics Year : 2020

On bifibrations of model categories

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Pierre Cagne
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Abstract

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.
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Dates and versions

hal-03103177 , version 1 (08-01-2021)

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Pierre Cagne, Paul-André Melliès. On bifibrations of model categories. Advances in Mathematics, 2020, 370, pp.107205. ⟨10.1016/j.aim.2020.107205⟩. ⟨hal-03103177⟩
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