Geodesic
Homotopy theories of diagrams
Theory and applications of categories, Tome 28 (2013), pp. 269-303

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

Suppose that S is a space. There is an injective and a projective model structure for the resulting category of spaces with S-action, and both are easily derived. These model structures are special cases of model structures for presheaf-valued diagrams $X$ defined on a fixed presheaf of categories E which is enriched in simplicial sets.

Varying the parameter category object E (or parameter space S) along with the diagrams X up to weak equivalence requires model structures for E-diagrams having weak equivalences defined by homotopy colimits, and a generalization of Thomason's model structure for small categories to a model structure for presheaves of simplicial categories.

Publié le :
Classification : Primary 18F20, Secondary 18G30, 55U35
Keywords: model structures, presheaves of categories, diagrams 
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J.F. Jardine. Homotopy theories of diagrams. Theory and applications of categories, Tome 28 (2013), pp. 269-303. http://geodesic.mathdoc.fr/item/TAC_2013_28_a10/