I was trying to read the paper "Equivariant minimal models" by G. Triantafillou(1982) and was trying to compute cohomology of a system of DGA with rational coefficient system. Given a finite group $G,$ let $\mathcal{O}_G$ be the category of canonical orbits. Let $\underline{V}$ be a dual rational coefficient system which is a covariant functor from $\mathcal{O}_G$ to rational vector spaces (denote this category by $Vec^*_G$). If I have a system of $DGA$, say $U$, then $$H^*(U;\underline{V})\cong H^*(Hom(\underline{V},U)).$$ Here, $Hom$ means of morphism in $Vec^*_G.$ By a spectral sequence $$E_2^{s,t}=Ext^s(\underline{V},\underline{H}^t(U)) \implies H^{s+t}(U,\underline{V}).$$ This is constructed by taking a projective resolution $\underline{V}^*$ of $\underline{V}$ and the double complex $Hom(\underline{V}^*,U).$ Here is my question:
How to take a projective resolution of $\underline{V}$?
From her paper, I could only see the existence of projective cover of a rational coefficient system $M$ which are contravariant functors from $\mathcal{O}_G$ to rational vector spaces (in this category she proved the existence of projective cover for every such functor). Since $\underline{V}$ is in $Vec^*_G,$ I am not able to find the projective resolution. Any reference where I can find such literature?
