We extend the formalisation of confluence results in Kleene algebras to a formalisation of coherent confluence proofs. For this, we introduce the structure of higher globular Kleene algebra, a higher-dimensional generalisation of modal and concurrent Kleene algebra. We calculate a coherent Church-Rosser theorem and a coherent Newman's lemma in higher Kleene algebras by equational reasoning. We instantiate these results in the context of higher rewriting systems modelled by polygraphs.

@article{paperbot1640,
  title = {Algebraic coherent confluence and higher globular Kleene algebras},
  author = {Cameron Calk and Eric Goubault and Philippe Malbos and Georg Struth},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 18, Issue 4},
  year = {2022},
  doi = {10.46298/lmcs-18(4:9)2022}
}