Minimal fibrations and the organizing theorem of simplicial homotopy theory

Details Minimal fibrations and the organizing theorem of simplicial homotopy theory Minimal fibrations and the organizing theorem of simplicial homotopy theory

2012-03-14

arxiv.org/abs/1203.3004v2

Mathematics

Algebraic Topology

Scientific paper

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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