The coordination of heterogeneous autonomous agents in dynamic, adversarial environments requires simultaneous satisfaction of geometric constraints, logical consistency, temporal reasoning, and strategic optimization. Existing sheaf- and topos-theoretic frameworks provide powerful tools for geometric consensus, knowledge alignment, and causal planning, but lack explicit models for value, reward, and strategic choice. This report presents a unified categorical framework that integrates event calculus, SCEL-like ensemble formation, and game-theoretic reward structures into a single Grothendieck topos of time-space histories. We introduce the notion of a \emph{game sheaf} whose stalks contain utility functions and policy distributions, and restriction maps encode both parallel transport and best-response dynamics. We prove that Nash equilibria correspond to global sections of a derived best-response correspondence sheaf, while cohomological obstructions classify failures of strategic consistency. A detailed case study of an immunological ``bastion defense'' scenario -- heterogeneous agents forming attack/defense ensembles under resource constraints -- demonstrates the framework's expressiveness. This synthesis provides a rigorous foundation for verifiable, autonomic, and economically rational multi-agent systems.

翻译：在动态、对抗性环境中异构自主智能体的协调需要同时满足几何约束、逻辑一致性、时间推理和战略优化。现有基于层与拓扑论的框架为几何共识、知识对齐和因果规划提供了强大工具，但缺乏对价值、奖励和战略选择的显式建模。本文提出一个统一的范畴论框架，将事件演算、类SCEL的集群形成和博弈论奖励结构整合到单个时空历史的格罗滕迪克拓扑中。我们引入“博弈层”概念，其茎包含效用函数和策略分布，限制映射既编码平行传输又编码最优反应动态。我们证明纳什均衡对应于导出最优反应对应层的整体截面，而同调障碍对战略一致性的失效进行分类。通过一个免疫学“堡垒防御”场景的详细案例研究——异构智能体在资源约束下形成攻击/防御集群——展示了该框架的表达能力。这一综合为可验证、自主且经济理性的多智能体系统提供了严格基础。