Propriétés universelles et extensions de Kan dérivées

Denis-Charles Cisinski

We prove that, given any small category A$=, the derivator HOT_A, corresponding to the homotopy theory of presheaves of homotopy types on A, is characterized by a natural universal property. In particular, the theory of Kan extensions extends to the setting of Grothendieck derivators.

Keywords: derivator, homotopy theory, derived Kan extension, homotopy colimit, homotopy limit

2000 MSC: 55U40, 18A40, 18G50, 18G55, 55U35

Theory and Applications of Categories, Vol. 20, 2008, No. 17, pp 605-649.

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