dg-Hecke Duality and Tensor Products

Abstract

We continue our study of the monoidal category $D(G)$ begun in [ 12]. At the level of cohomology we transfer the duality functor $R\underline{\operatorname{Hom}}(-,k)$ to the derived category of dg-modules $D(H_{U}^{\bullet })$. In the process we develop a more general and streamlined approach to the anti-involution $\mathscr J$ from [ 8]. We also verify that the tensor product on $D(G)$ corresponds to an operadic tensor product on the dg-side (cf [ 5]). This uses a result of Schnürer on dg-categories with a model structure.