Comodules, Matrix Coefficients, and Coalgebra Duality — Examples

Build group-graded vector spaces as kG-comodules, compute two-dimensional coefficient matrices, and exhibit why an arbitrary C*-module need not reconstruct a coaction when C is infinite.

These are planned worked examples and counterexamples for comodules-matrix-coefficients-and-coalgebra-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.