On the equivalence of AQFTs and prefactorization algebras

Abstract This paper revisits the equivalence problem between algebraic quantum field theories and prefactorization algebras defined over globally hyperbolic Lorentzian manifolds. We develop a radically new approach whose main innovative features are 1. ) a structural implementation of the additivity property used in earlier approaches and 2. ) a reduction of the global equivalence problem to a family of simpler spacetime-wise problems. When applied to the case where the target category is a symmetric monoidal 1-category, this yields a generalization of the equivalence theorem from Commun. Math. Phys. 377, 971 (2019). In the case where the target is the symmetric monoidal ∞ -category of cochain complexes, we obtain a reduction of the global ∞ -categorical equivalence problem to simpler, but still challenging, spacetime-wise problems. The latter would be solved by showing that certain functors between 1-categories exhibit ∞ -localizations; however, the available detection criteria are inconclusive in our case.