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

@article{AIF_1997__47_5_1491_0,
     author = {Golasi\'nski, Marek},
     title = {Injective models of $G$-disconnected simplicial sets},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {47},
     number = {5},
     year = {1997},
     pages = {1491-1522},
     doi = {10.5802/aif.1607},
     zbl = {0886.55012},
     mrnumber = {99b:55020},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1997__47_5_1491_0}
}
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/item/AIF_1997__47_5_1491_0/

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