Let $G$ be a finite group, $X$ a $G$-simplical set (not necessary $G$-connected) and $\widetilde{mathcal O}(G,X)$ the associated category with objects given by pairs $(G/H,x)$ for any subgroup $H\subseteq G$ and a $0$-simplex $x\in X^H_0$, where $X^H$ is the fixed point simplicial subset of $X$. We show that for the $\widetilde{\mathcal O}(G,X)$-system of de-Rham algebras $\mathcal{A}_X$ on $X$ there is its injective minimal model $\mathcal{M}_X$ encodding the rational homotopy information on $X$ via the Postnikov tower of $X$. Approching of cofibrant minimal models of $\mathcal{A}_X$  is also planed provided $G$ is a Hamiltonian finite group.