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：我们为因果关系、非局域性和语境性研究提供了一个统一的运算框架，该框架完全独立于设备和理论。本工作根植于Abramsky和Brandenburger提出的层论语境性框架，并将其扩展至包含任意因果序（无论是确定的、动态的还是不确定的）。我们定义了输入历史任意空间上的因果函数概念，并证明了对联合输出施加明确因果约束等价于对输入历史的末端事件自由分配局部输出。我们证明了因果函数在底层空间上的并行、顺序和条件顺序组合中的分解结果。我们证明因果关系等价于相对于底层空间下集拓扑的连续性，并展示了在开子空间上定义的局部因果函数可捆绑为预层。然而，与Abramsky-Brandenburger框架显著不同的是，我们证明因果函数在某些情况下无法构成层。我们针对输入历史空间任意开覆盖，将实证模型定义为因果函数概率分布预层中的相容族。我们展示了因果诱导语境性的存在——当因果约束本身变得依赖语境时出现的现象——并证明了全序（包括静态与动态）上非局域性的不可行结果。