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%%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: Letter %%EndSetup %%Page: 58 1 58 0 bop 1505 790 a Fs(CHAPTER)51 b(2)147 1089 y Fr(Hopf)45 b(Algebras,)h(Algebraic,)g(F)-11 b(ormal,)45 b(and)g(Quan)l(tum)g (Groups)1762 5365 y Fq(58)p eop %%Page: 59 2 59 1 bop 1028 236 a Fq(6.)35 b(QUANTUM)e(A)n(UTOMORPHISM)e(GR)n(OUPS) 925 b(59)915 425 y Fp(6.)56 b(Quan)m(tum)37 b(Automorphism)f(Groups)149 600 y(Lemma)i(2.6.1.)49 b Fo(The)34 b(c)-5 b(ate)g(gory)35 b Fn(K)17 b Fo(-)6 b Fp(Alg)34 b Fo(of)h Fn(K)17 b Fo(-algebr)-5 b(as)40 b(has)34 b(arbitr)-5 b(ary)35 b(c)-5 b(opr)g(o)g(ducts.)149 777 y Fm(Pr)n(oof.)42 b Fs(This)31 b(is)e(a)h(w)m(ell)g(kno)m(wn)h (fact)f(from)f(univ)m(ersal)h(algebra.)41 b(In)31 b(fact)f(all)e (equationally)0 893 y(de\014ned)34 b(algebraic)c(categories)j(are)f (complete)f(and)i(co)s(complete.)42 b(W)-8 b(e)33 b(indicate)e(the)i (construc-)0 1009 y(tion)f(of)g(the)h(copro)s(duct)g(of)f(a)g(family)e (\()p Fl(A)1539 1024 y Fk(i)1567 1009 y 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