Exploring Homotopies in Multiway Rewriting Systems
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11mo ago· 2 min readenInsight
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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.
We investigate algebraic and compositional properties of abstract multiway rewriting systems, which are archetypical structures underlying the formalism of the Wolfram model. We demonstrate the existence of higher homotopies in this class of rewriting sys
