Witt equivalence of global fields

A Simplicial derivation procedure for crossed module valued functors is established. As a consequence, a theory of higher Baer invariants and relative homology is settle on crossed modules. Then we illustrative how this method is efficient, as it extends classical formulations and results, like various known five term sequences on crossed modules by Conduché and Ellis (1989), the author (1993) and Ladra and R-Grandjeán (1994).