Abstract
Quillen showed that simplicial sets form a model category (with appropriate choices of three classes of morphisms), which organized the homotopy theory of simplicial sets. His proof is very difficult and uses even the classification theory of principal bundles. Thus, Goerss–Jardine appealed to topological methods for the verification. In this paper we give a new proof of this organizing theorem of simplicial homotopy theory which is elementary in the sense that it does not use the classifying theory of principal bundles or appeal to topological methods.
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The author would like to thank Prof. N. Oda for his valuable comments on an earlier version of this paper.
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Communicated by Prof. Salvatore Rionero.
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Kihara, H. Minimal fibrations and the organizing theorem of simplicial homotopy theory. Ricerche mat. 63, 79–91 (2014). https://doi.org/10.1007/s11587-013-0165-5
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DOI: https://doi.org/10.1007/s11587-013-0165-5