We introduce a polarized 2-categorical framework equipped with a non-involutive generative negation defined as a strict 2-endofunctor acting on objects, 1-morphisms, and 2-morphisms. Unlike classical and linear logical negation, this operation is not truth-functional and does not satisfy involutivity. Instead, it generates non-trivial higher morphism structure, leading to a failure of coherence in general 2-categorical settings. We prove that no strict 2-functor into an involutive 2-category can preserve both the generative negation and the associated tensor structure up to coherent isomorphism. We further show that this framework is incompatible with standard linear logic dualities, demonstrating a structural obstruction to embedding into classical or paraconsistent logical systems. The results suggest a higher-categorical interpretation of negation as a generative transformation rather than a truth-value operation.
Yugo Hidaka (Mon,) studied this question.