# Categorification of algebraic quantum field theories

March 30, 2020

This paper develops a novel concept of 2-categorical algebraic quantum field
theories (2AQFTs) that assign locally presentable linear categories to
spacetimes. It is proven that ordinary AQFTs embed as a coreflective full
2-subcategory into the 2-category of 2AQFTs. Examples of 2AQFTs that do not
come from ordinary AQFTs via this embedding are constructed by a local gauging
construction for finite groups, which admits a physical interpretation in terms
of orbifold theories. A categorification of Fredenhagen's universal algebra is
developed and also computed for simple examples of 2AQFTs.

Keywords:

algebraic quantum field theory, 2-categories, 2-operads, quasi-coherent sheaves, locally presentable linear categories, categorified orbifold theories, local-to-global extensions