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

Key Points

• This work aims to explore how classical logic arises from higher-categorical structures and the effects of truncation and negation.
• Investigated higher-order structures in classical categorical settings.
• Introduced stratified negation in weak 2-categories.
• Illustrated concepts with examples from homotopy theory.
• Demonstrated that certain higher-order structures cannot be faithfully represented in classical settings.
• Proved that stratified negation is not preserved in strict or pseudo embeddings.
• Used homotopy theory to show how higher structure collapses under truncation.