Weak enriched categories - Catégories enrichies faibles.

Regis Pellissier (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

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 à 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.

Mots clés: catégorie de Segal; catégorie enrichie; groupoïde fondamental; n-catégorie; réalisation géométrique

Domaines: Topologie algébrique [math.AT]; Catégories et ensembles [math.CT]; Géométrie algébrique [math.AG]

Regis Pellissier. Weak enriched categories - Catégories enrichies faibles.. Topologie algébrique [math.AT]. Université Nice Sophia Antipolis, 2002. Français. ⟨NNT : ⟩. ⟨hal-00000565⟩