Homotopies in Multiway (Nondeterministic) Rewriting Systems as n-Fold Categories
Homotopies in Multiway (Nondeterministic) Rewriting Systems as n-Fold Categories
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 systems, where homotopical maps are induced by the inclusion of appropriate rewriting rules taken from an …