Contents 1. Introduction 2 2. Preliminaries 4 2.1. Some results on ...

163( )Proof. Since (Q B , p Q ) = Coequ Fun µBQ BU, Q B Uλ B we have that))(p QB ̂QA ) ◦(µ B QBU B ̂QA = (p QB ̂QA ) ◦(Q B Uλ BB ̂QAso that we obtain) )(p QB ̂QA ◦(Qpb Q(107)== (p QB ̂QA ) ◦ (Q B µb QA)(◦ χ ̂Q) )χ=A U(p QB ̂QA ◦(χ ̂Q) )A ◦(QP Qpb Q) (p QB ̂QA ◦(µ B ̂Q)Q A ◦(Qy ̂Q) )A ◦(QP Qpb Q(Qy ̂Q) )A ◦(QP Qpb Q) ((QBpb Q◦ Qy ̂Q)A U) ) ( ) ((p QB ̂QA ◦(Qpb Q◦ Q B µb Q AU ◦ Qy ̂Q)A U= (p QB ̂QA ) ◦ (Q B µb QA) ◦y(175)== (p QB ̂QA ) ◦ (Q B µb QA) ◦and hence we get) ) ((193)(p QB ̂QA ◦(Qpb Q◦ χ ̂Q)A U =) ) ( ) ((p QB ̂QA ◦(Qpb Q◦ Q B µb Q AU ◦ Qy ̂Q)A Uso that) )(p QB ̂QA ◦(Qpb Q◦ (Ql A U) ◦ (QP x A U) ◦ (χP QP A U)) ) (χ=(p QB ̂QA ◦(Qpb Q◦ χ ̂Q)A U ◦ (QP Ql A U) ◦ (QP QP x A U)) ) ( ) ((193)=(p QB ̂QA ◦(Qpb Q◦ Q B µb Q AU ◦ Qy ̂Q)A U ◦ (QP Ql A U) ◦ (QP QP x A U)) ) ( )y=(p QB ̂QA ◦(Qpb Q◦ Q B µb Q AU ◦ (QBl A U) ◦ (QyP A A U) ◦ (QP QP x A U)) )(190)=(p QB ̂QA ◦(Qpb Q◦ (Ql A U) ◦ (QP x A U) ◦ (QP χP A U) .Therefore we deduce that) )(194)(p QB ̂QA ◦(Qpb Q◦ (Ql A U) ◦ (QP x A U) ◦ (χP QP A U)) )=(p QB ̂QA ◦(Qpb Q◦ (Ql A U) ◦ (QP x A U) ◦ (QP χP A U)By using this equality we compute) ) (p QB ̂QA ◦(Qpb Q◦ (Ql A U) ◦ (QP u AA U) ◦ ( w l AU ) ◦ ( QP Cε C AU )) )w=(p lQB ̂QA ◦(Qpb Q◦ (Ql A U) ◦ (QP u AA U) ◦ ( QP ε C AU ) ◦ ( w l C A U )) )(103)=(p QB ̂QA ◦(Qpb Q◦ (Ql A U) ◦ (QP x A U) ◦ (QP δ C A U) ◦ ( w l C A U )) )w=(p lQB ̂QA ◦(Qpb Q◦ (Ql A U) ◦ (QP x A U) ◦ ( w l QP A U ) ◦ (QP Cδ C A U)) )=(p QB ̂QA ◦(Qpb Q◦ (Ql A U) ◦ (QP x A U) ◦ (χP QP A U) ◦ (QP δ C QP A U)◦ (QP Cδ C A U)