  Cycle sets are known to give non-degenerate unitary solutions of the
Yang--Baxter equation and linear cycle sets are enriched versions of these
algebraic systems. The paper explores the recently developed cohomology and
extension theory for linear cycle sets. We derive a four term exact sequence
relating 1-cocycles, second cohomology and certain groups of automorphisms
arising from central extensions of linear cycle sets. This is an analogue of a
similar exact sequence for group extensions known due to Wells. We also compare
the exact sequence for linear cycle sets with that for their underlying abelian
groups and discuss generalities on dynamical 2-cocycles.
