Weak enriched categories - Categories enrichies faibles

Details Weak enriched categories - Categories enrichies faibles Weak enriched categories - Categories enrichies faibles

2003-08-26

arxiv.org/abs/math/0308246v1

Mathematics

Algebraic Topology

Thesis, Universite de Nice - Sophia Antipolis (2002-06-27)

Scientific paper

This thesis is devoted to the proof of a theorem showing the existence of a closed model category structure for weakly enriched categories. It requires first of all the definitions of weakly enriched categories and equivalences of weakly enriched categories such that these definitions recover some existing notions of higher order weak categories, for example Segal categories, Tamsamani n-categories and strict n-categories. In order to prove our theorem, we elaborate a theory of plans for cell addition following the approach of the small object argument a la Quillen. We conclude this work with the proof that our theorem recovers the case of Segal categories. This last result requires a fundamental groupoid-geometric realization adjunction between Segal groupoids and topological spaces.

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