The discussion centers on the relevance of higher category theory, particularly n-categories, in physics, as articulated by Patricia Ritter. Participants highlight how categorical identities facilitate the equivalence of different integral orderings over volumes, leading to a categorical formulation of higher gauge theory. The conversation emphasizes the necessity of connecting advanced mathematics to tangible physical problems, with references to works by Lawvere and recent developments in quantum field theory and solid-state physics. The consensus is that while higher category theory may seem abstract, its applications in physics, especially in areas like topological phases and gauge theory, warrant further exploration.
PREREQUISITESPhysicists, mathematicians, and researchers interested in the intersection of advanced mathematics and physical theories, particularly those exploring gauge theory, quantum field theory, and solid-state physics.
[URL='https://www.physicsforums.com/insights/author/urs-schreiber/']Urs Schreiber[/URL] said:Remarkably, homotopy theory is a "smaller theory": it arises from classical theory by removing axioms from classical logic. This is the fantastic insight of homotopy type theory.