Minimal resolutions and other minimal models.

Agustí Roig

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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 $E I$ -category $𝕀$ . We then make use of the $E I$ -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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