On bifibrations of model categories
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.
Domains
Computer Science [cs] Logic in Computer Science [cs.LO] Computer Science [cs] Computation and Language [cs.CL] Mathematics [math] Quantum Algebra [math.QA] Mathematics [math] Algebraic Geometry [math.AG] Computer Science [cs] Computer Science and Game Theory [cs.GT] Computer Science [cs] Mathematical Software [cs.MS] Computer Science [cs] Formal Languages and Automata Theory [cs.FL] Computer Science [cs] Programming Languages [cs.PL] Mathematics [math] Category Theory [math.CT] Mathematics [math] Logic [math.LO] Mathematics [math] Algebraic Topology [math.AT]
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