Recent advances in artificial intelligence reveal the limits of purely predictive systems and call for a shift toward causal and collaborative reasoning. Drawing inspiration from the revolution of Grothendieck in mathematics, we introduce the relativity of causal knowledge, which posits structural causal models (SCMs) are inherently imperfect, subjective representations embedded within networks of relationships. By leveraging category theory, we arrange SCMs into a functor category and show that their observational and interventional probability measures naturally form convex structures. This result allows us to encode non-intervened SCMs with convex spaces of probability measures. Next, using sheaf theory, we construct the network sheaf and cosheaf of causal knowledge. These structures enable the transfer of causal knowledge across the network while incorporating interventional consistency and the perspective of the subjects, ultimately leading to the formal, mathematical definition of relative causal knowledge.

翻译：人工智能的最新进展揭示了纯预测系统的局限性，并呼吁向因果与协作推理转变。受格罗滕迪克数学革命的启发，我们提出了因果知识的相对性，其核心观点是结构因果模型本质上是嵌入关系网络中的不完美、主观的表征。通过运用范畴论，我们将结构因果模型组织为函子范畴，并证明其观测概率测度与干预概率测度自然构成凸结构。这一结果使我们能够用概率测度的凸空间来编码未干预的结构因果模型。接着，利用层理论，我们构建了因果知识的网络层与余层。这些结构使得因果知识能够在网络中传递，同时融入干预一致性与主体视角，最终形成了相对因果知识的严格数学定义。