  This paper develops a 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.
