Minimal fibrations and the organizing theorem of simplicial homotopy theory

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 topol...

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Bibliographic Details
Published in:Ricerche di matematica 2014-06, Vol.63 (1), p.79-91
Main Author: Kihara, Hiroshi
Format: Article
Language:English
Subjects:
Algebra
Analysis
Geometry
Mathematics
Mathematics and Statistics
Numerical Analysis
Probability Theory and Stochastic Processes
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Summary: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.
ISSN:0035-5038
1827-3491
DOI:10.1007/s11587-013-0165-5