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arXiv · 2606.19525

A Categorial and Sheaf-Theoretic Semantics for Autonomic Component Ensembles

Manuel Hernández·Eduardo Sánchez-Soto
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Abstract

The proliferation of large-scale, decentralized systems of autonomous agents, such as swarms of robots and networked cyber-physical systems, presents a formidable challenge to traditional formal methods. The Software Component Ensemble Language (SCEL) offers a formal model for such systems, but its operational semantics is not ideal for reasoning about global, structural, and emergent properties. This report proposes a new, multi-layered mathematical model for SCEL using category theory and sheaf theory. We argue that a society of robots described in SCEL can be formally modeled as a sheaf on a topological space, where components are points, ensembles are open sets, and distributed knowledge forms the sheaf's data. In this framework, computational processes like information sharing become equivalent to the sheaf-theoretic operation of "gluing" local data. System failures can then be understood and quantified as topological obstructions, measurable by sheaf cohomology. This approach transforms the verification of a complex distributed system into the analysis of the geometry of a mathematical object, providing deep, structural insights for the design of robust autonomic systems.

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Manuel Hernández, Eduardo Sánchez-Soto. 2026-06-17. A Categorial and Sheaf-Theoretic Semantics for Autonomic Component Ensembles. https://arxiv.org/abs/2606.19525

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