Seminar of Algebra

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Towards homotopy theory of model categories

Boris Chorny (University of Haifa)
Departamento de Álgebra
Mon, 28 mar 2016 12:30
Boris Chorny is a lecturer at the University of Haifa at Oranim. His main area of interest is Homotopy theory. More specifically, homotopical localizations, Goodwillie calculus, and Brown representability.

We will show that every Quillen equivalence of two (simplicial, combinatorial) model categories A and B with all objects cofibrant induces a Quillen equivalence of the categories of homotopy functors from A and B into simplicial sets.

This theorem may be viewed as model theoretic interpretation of a theorem by Dwyer and Kan. On the other hand, it indicates that there should exist a sound homotopy theory of model categories.

We intend to discuss why homotopy theory of homotopy theories (presented nowadays in plenty different models) does not give a satisfactory description of homotopy theory of model categories.