ACM Transactions on Computational Logic· 2026Q2
Layered Monoidal Theories I: Diagrammatic Algebra and Applications
- 2citations
- Q2SCImago
- 2026year
Short summary
A new framework, layered monoidal theories, allows mixing formal descriptions of systems at different abstraction levels within a single string diagram, preserving mathematical rigor.
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Key points
- Introduces layered monoidal theories, a generalization of monoidal theories.
- Allows mixing multiple monoidal theories and translations within a single string diagram.
- Maintains mathematical precision and semantic interpretability.
- Provides a graphical formalism for reasoning about information flow across different scientific fields.
AI-generated from the title and abstract; the full text is not read.
Abstract
We develop layered monoidal theories – a generalisation of monoidal theories combining formal descriptions of a system at different levels of abstraction. Via their representation as string diagrams , monoidal theories provide a graphical formalism to reason algebraically about information flow in models across different fields of science. Layered monoidal theories allow mixing several monoidal theories (together with translations between them) within the same string diagram, while retaining mathematical precision and semantic interpretability. We develop the mathematical foundations of layered monoidal theories, as well as providing several instances of our approach, including digital and electrical circuits, quantum processes, chemical reactions, concurrent processes, and probability theory.
The authors' abstract, as published at the source. ACM Transactions on Computational Logic, 2026 · DOI ↗
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