标题： 关于AQFT和预因子代数的等价性 显示英文标题

标题： On the equivalence of AQFTs and prefactorization algebras

摘要： 本文重新审视了定义在全局双曲洛伦兹流形上的代数量子场论与预因子化代数之间的等价性问题。 我们提出了一种全新的方法，其主要创新之处在于1.) 对先前方法中使用的可加性性质的结构化实现，以及2.) 将全局等价性问题简化为一系列更简单的时空局部问题。 当目标范畴是一个对称单子$1$-范畴时，这给出了[Commun. Math. Phys. 377, 971 (2019)]中等价定理的一个推广。 在目标为对称单子$\infty$-范畴的共链复形情况下，我们得到了将全局$\infty$-范畴等价性问题简化为更简单但仍然具有挑战性的时空局部问题。 后者可以通过证明某些在$1$-范畴之间的函子表现出$\infty$-局部化来解决，然而目前可用的检测标准在我们的情况下并不明确。 显示英文摘要

摘要： 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 $\infty$-category of cochain complexes, we obtain a reduction of the global $\infty$-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 $\infty$-localizations, however the available detection criteria are inconclusive in our case.