Group cohomology and its computation renders a computationally efficient model to work with techniques defined for more generic settings in homological algebra. Thus, the basic calculational schemes already incorporated in Magma for the computation of group cohomology form a good illustration to a more generic workflow for computation of cohomologies in other modular categories - Lie algebras, Affine algebras, etc.

We shall discuss the basics of computing cohomology rings, and look into current research on computation of homotopy invariants applicable to these rings: most specifically, we shall look at computation of A-infinity products in group and basic algebra cohomology.