Simplicial and categorical diagrams, and their equivariant applications

Rudolf Fritsch and Marek Golasinski

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.

Theory and Applications of Categories, Vol. 4, 1998, No. 4, 73-81
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