Exploring Homotopies in Multiway Rewriting Systems
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Summary
The article explores the algebraic and compositional properties of abstract multiway rewriting systems, demonstrating the existence of higher homotopies and their formalization as $n$-fold categories. It discusses the inclusion of appropriate rewriting rules and the potential connections to homotopy spaces relevant to physics.
Key quotes
· 3 pulledWe demonstrate the existence of higher homotopies in this class of rewriting systems.
A multiway rewriting system with homotopies up to order $n$ may naturally be formalized as an $n$-fold category.
This computational framework of homotopical multiway systems may potentially be used for making formal connections to homotopy spaces upon which models relevant to physics may be instantiated.
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