This paper displays an approach to the construction of the homotopy theory of simplicial sets and the corresponding equivalence with the homotopy theory of topological spaces which is based on simplicial approximation techniques. The required simplicial approximation results for simplicial sets and their proofs are given in full. Subdivision behaves like a covering in the context of the techniques displayed here.
Keywords: simplicial sets, simplicial approximation, model structures
2000 MSC: 55U10, 18G30, 55U35
Theory and Applications of Categories,
Vol. 12, 2004,
No. 2, pp 34-72.
http://www.tac.mta.ca/tac/volumes/12/2/12-02.dvi
http://www.tac.mta.ca/tac/volumes/12/2/12-02.ps
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Revised 2005-11-20. Original version at
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