Hopf Module Tensor Products and Rigid Duality — Examples

Work out a finite-group contragredient and a Taft module dual; demonstrate that tensor products require only a bialgebra, whereas duals use the antipode and finite dimensionality.

These are planned worked examples and counterexamples for hopf-module-tensor-products-and-rigid-duality, with empty item lists pending normal authoring and proof review. Each example must calculate from the stated hypotheses, and each counterexample must verify both its premises and the failed conclusion. This companion is a dependency leaf and supplies no theorem to another page.