Geodesic
Simplicial and categorical diagrams, and their equivariant applications
Theory and applications of categories, Tome 4 (1998), pp. 73-81

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

We show that the homotopy category of simplicial diagrams $I-SS$ indexed by a small category $I$ is equivalent to a homotopy category of $SS\downarrow NI$ simplicial sets over the nerve $NI$. Then their equivalences, by means of the nerve functor N : Cat --> SS$ from the category $Cat$ of small categories, with respective homotopy categories associated to $Cat$ are established. Consequently, an equivariant simplicial version of the Whitehead Theorem is derived.

Classification : Primary 55P15, 55U10, secondary 18G30, 55P91.
Keywords: comma category, Grothendieck construction, homotopy colimit, pull-back, simplicial set, small category. 
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     author = {Rudolf Fritsch and Marek Golasinski},
     title = {Simplicial and categorical diagrams, and their equivariant applications},
     journal = {Theory and applications of categories},
     pages = {73--81},
     publisher = {mathdoc},
     volume = {4},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_1998_4_a3/}
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Rudolf Fritsch; Marek Golasinski. Simplicial and categorical diagrams, and their equivariant applications. Theory and applications of categories, Tome 4 (1998), pp. 73-81. http://geodesic.mathdoc.fr/item/TAC_1998_4_a3/