We provide a unified operational framework for the study of causality, non-locality and contextuality, in a fully device-independent and theory-independent setting. Our work has its roots in the sheaf-theoretic framework for contextuality by Abramsky and Brandenburger, which it extends to include arbitrary causal orders (be they definite, dynamical or indefinite). We define a notion of causal function for arbitrary spaces of input histories, and we show that the explicit imposition of causal constraints on joint outputs is equivalent to the free assignment of local outputs to the tip events of input histories. We prove factorisation results for causal functions over parallel, sequential, and conditional sequential compositions of the underlying spaces. We prove that causality is equivalent to continuity with respect to the lowerset topology on the underlying spaces, and we show that partial causal functions defined on open sub-spaces can be bundled into a presheaf. In a striking departure from the Abramsky-Brandenburger setting, however, we show that causal functions fail, under certain circumstances, to form a sheaf. We define empirical models as compatible families in the presheaf of probability distributions on causal functions, for arbitrary open covers of the underlying space of input histories. We show the existence of causally-induced contextuality, a phenomenon arising when the causal constraints themselves become context-dependent, and we prove a no-go result for non-locality on total orders, both static and dynamical.

翻译：我们为因果性、非定域性和情境性研究提供了一个统一的操作框架，该框架完全独立于设备与理论假设。本研究根植于Abramsky和Brandenburger提出的层论框架，并将其扩展至包含任意因果序（无论是确定的、动态的还是非确定的）。我们针对输入历史空间的任意结构定义了因果函数概念，并证明了对联合输出显式施加因果约束等价于将局部输出自由分配给输入历史中的顶端事件。我们给出了因果函数在底层空间的并行、序贯及条件序贯组合上的分解定理。证明了因果性等价于关于底层空间下集拓扑的连续性，并揭示了定义于开子空间上的偏因果函数可捆绑成预层。然而，与Abramsky-Brandenburger框架显著不同的是，我们展示了在某些条件下因果函数无法形成层。我们将经验模型定义为因果函数概率分布预层中关于输入历史空间任意开覆盖的相容族。论证了因果诱导情境性的存在——即因果约束本身变得依赖于情境的现象，并证明了在全序（包括静态与动态情形）上非定域性的不可行定理。