Injective models of G-disconnected simplicial sets
Annales de l'Institut Fourier, Volume 47 (1997) no. 5, pp. 1491-1522.

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.

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

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Golasiński, Marek. Injective models of $G$-disconnected simplicial sets. Annales de l'Institut Fourier, Volume 47 (1997) no. 5, pp. 1491-1522. doi : 10.5802/aif.1607. http://www.numdam.org/articles/10.5802/aif.1607/

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