Geodesic
Propriétés universelles et extensions de Kan dérivées
Theory and applications of categories, Tome 20 (2008), pp. 605-649.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.
Classification : 55U40, 18A40, 18G50, 18G55, 55U35
Keywords: derivator, homotopy theory, derived Kan extension, homotopy colimit, homotopy limit 
@article{TAC_2008_20_a16,
     author = {Denis-Charles Cisinski},
     title = {Propri\'et\'es universelles et extensions de {Kan} 
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     journal = {Theory and applications of categories},
     pages = {605--649},
     publisher = {mathdoc},
     volume = {20},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2008_20_a16/}
}
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Denis-Charles Cisinski. Propriétés universelles et extensions de Kan 
dérivées. Theory and applications of categories, Tome 20 (2008), pp. 605-649. http://geodesic.mathdoc.fr/item/TAC_2008_20_a16/