Dear All Let $R$ be a commutative ring, $G$ a group, $\mathrm{Mod}_R$ the category of $R$-modules, $\mathrm{Mod}_{RG}$ that of right $RG$-modules, let \[ \mathcal G\colon \mathrm{Mod}_{R}\longrightarrow \mathrm{Mod}_{RG} \] be the familiar functor which assigns to the $R$-module $V$ the right $RG$-module $\mathrm{Map}(G, V)$, with right $G$-structure being given by left translation in $G$, and let \[ \square \colon \mathrm{Mod}_{RG}\longrightarrow \mathrm{Mod}_{R} \] be the forgetful functor. The unit of the resulting adjunction is well known to be given by the assignment to the right $RG$-module $V$ of \[ \eta_V\colon V \longrightarrow \mathrm{Map}(G, \square V), \ v \longmapsto \eta_v:G \to \square V,\ \eta_v(x) =vx, \ v \in V, x \in G. \] Given the $RG$-module $V$, the standard construction associated with $V$ and the resulting monad $(T,\eta,\mu)$ yields an injective resolution of $V$ in the category of right $RG$-modules. All this is entirely standard and classical. Consider instead the functor \[ \mathrm{Mod}_{RG}\longrightarrow \mathrm{Mod}_{RG} \] which assigns to the right $RG$-module $V$ the right $RG$-module $\mathrm{Map}(G, V)$, with right $G$-structure being given by diagonal action relative to left translation in $G$ and replace $\eta$ with $\omega$ given by the assignment to the right $RG$-module $V$ of \[ \omega_V\colon V \longrightarrow \mathrm{Map}(G, V), \ v \longmapsto \omega_v:G \to V,\ \omega_v(x) =v, \ v \in V, x \in G. \] These data, together with the appropriate natural transformation replacing the composition $\mu$, yield an alternate description of the monad $(T,\eta,\mu)$. This has certainly been discussed in detail in the literature. I am looking for a precise reference. Many thanks in advance Johannes HUEBSCHMANN Johannes Professeur de Mathematiques USTL, UFR de Mathematiques UMR 8524 Laboratoire Paul Painleve F-59 655 Villeneuve d'Ascq Cedex France http://math.univ-lille1.fr/~huebschm TEL. (33) 3 20 43 41 97 (33) 3 20 43 42 33 (secretariat) (33) 3 20 43 48 50 (secretariat) Fax (33) 3 20 43 43 02 e-mail Johannes.Huebschmann@math.univ-lille1.fr