Truncation, Negation, and Coherence Obstructions in Higher-Categorical Logic

This work investigates how classical logic emerges from higher-categorical structures via truncation. We show that certain higher-order structures cannot be faithfully represented in classical categorical settings.We introduce a notion of stratified negation in weak 2-categories and prove that it cannot be preserved under strict or pseudo embeddings into locally discrete categories.An example from homotopy theory illustrates the collapse of higher structure under truncation.