Quandle cohomology, extensions and automorphisms

A quandle is an algebraic system with a binary operation satisfying three axioms modelled on the Reidemeister moves of planar diagrams links in 3-space. The paper establishes new relationship between cohomology, extensions and automorphisms quandles. We derive four term exact sequence relating 1-cocycles, second cohomology certain group abelian extension non-abelian counterpart this involving dynamical classes also established, some applications to lifting are given. Viewing construction conjugation, core generalised Alexander as adjoint functor appropriate from category quandles groups, we prove that these functors map groups Finally, construct natural homomorphisms its conjugation