Categorical Aspects of Algebraic Quantum Field Theory - Perin, Marco (2022)
The aim of this work is to introduce and investigate 3 distinct problems in Algebraic Quantum Field Theory whose solution relies on (higher) multicategorical methods. More precisely, we will discuss a model-independent comparison between Algebraic Quantum Field Theory and Factorization Algebras, a 2-categorical notion of algebraic quantum field theory more sensitive to global aspects of gauge theories than previous approaches and a ``smoothness axiom'' for algebraic quantum field theories encoding ``smooth responses of observable algebras'' to ``smooth variations of spacetimes''.