Injective models of $G$-disconnected simplicial sets

Golasiński, Marek

Annales de l'Institut Fourier, Tome 47 (1997) no. 5, pp. 1491-1522.

Nous généralisons les résultats de G.V. Triantafillou et B. Fine sur les ensembles simpliciaux $G$-non connexes. On présente l’existence d’un modèle injectif minimal pour une $𝕀$-algèbre complète, où $𝕀$ est une $EI$-catégorie. Ensuite, nous utilisons la $EI$-catégorie $𝒪(G,X)$ associée à un $G$-ensemble simplicial $X$, pour appliquer ces résultats à la catégorie des $G$-ensembles simpliciaux.

Enfin, nous décrivons le $G$-type d’homotopie rationnelle d’un $G$-ensemble simplicial nilpotent en utilisant leur modèle injectif minimal

We generalize the results by G.V. Triantafillou and B. Fine on $G$-disconnected simplicial sets. An existence of an injective minimal model for a complete $𝕀$-algebra is presented, for any $EI$-category $𝕀$. We then make use of the $EI$-category $𝒪(G,X)$ associated with a $G$-simplicial set $X$ to apply these results to the category of $G$-simplicial sets.

Finally, we describe the rational homotopy type of a nilpotent $G$-simplicial set by means of its injective minimal model.

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