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Published in:
2009 | OriginalPaper | Chapter
Simplicial functors and homotopy coherence
Authors : Paul G. Goerss, John F. Jardine
Published in: Simplicial Homotopy Theory
Publisher: Birkhäuser Basel
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Suppose that
A
is a simplicial category. The main objects of study in this chapter are the functors
X: A
→ S taking values in simplicial sets, and which respect the simplicial structure of
A
. In applications, the simplicial category
A
is typically a resolution of a category
I
, and the simplicial functor
X
describes a homotopy coherent diagram. The main result of this chapter (due to Dwyer and Kan, Theorem 2.13 below) is a generalization of the assertion that simplicial functors of the form
X: A
→ S are equivalent to diagrams of the form
I
→ S in the case where
A
is a resolution of the category
I
. The proof of this theorem uses simplicial model structures for categories of simplicial functors, given in Section 1, and then the result itself is proved in Section 2.