Methods for proving nonexistence of valued minion homomorphisms

Develop techniques to prove nonexistence of valued minion homomorphisms between specific pairs of templates (for example, from Plu(A,B) to projection-like minions), enabling robust hardness transfers and separations.

Background

Hardness results via the reduction theorem rely on demonstrating that certain homomorphisms do not exist. Systematic methods for such nonexistence proofs are underdeveloped in the valued setting, especially with plurimorphisms.

Creating general tools (invariants, obstructions, or algebraic certificates) would strengthen the framework’s ability to capture inapproximability.