2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74439We construct solutions to the set-theoretic Yang-Baxter equation using braid group representations in free group automorphisms and their Fox differentials. The method resembles the extensions of groups and quandles.Dedicated to Professor Louis H. Kauffman for his 60th birthdayGeometric TopologyQuantum Algebra57M05, 57M25text