Confluence of algebraic rewriting systems

Abstract Convergent rewriting systems on algebraic structures give methods to solve decision problems, prove coherence results, and compute homological invariants. These are based higher-dimensional extensions of the critical branching lemma that proves local confluence from branchings. The analysis structures, such as groups or linear algebras, is complicated because underlying axioms. This article introduces structure polygraph modulo formalizes interaction between rules an system inherent axioms, we show a for polygraphs. We deduce models whose axioms specified by convergent systems. illustrate our constructions string, linear, group