Infinity-categorical equivalence between PFAs and AQFTs

Establish a full proof of an infinity-categorical generalization of the equivalence between suitable categories of prefactorization algebras (PFAs) and algebraic quantum field theories (AQFTs), extending the 1-categorical equivalence result to the infinity-categorical setting.

Background

The paper reviews known relationships among different axiomatizations of quantum field theory in Lorentzian geometry. An example-independent equivalence theorem between prefactorization algebras and algebraic quantum field theories has been proven at the 1-categorical level, providing a solid bridge between these frameworks.

Recent work has made progress toward lifting this equivalence to an infinity-categorical framework, which is more natural for many modern homotopical and higher-categorical structures arising in quantum field theory. However, the authors note that a complete proof at the infinity-categorical level has not yet been achieved, identifying this as an explicit outstanding task in the literature.