Definition (Morphism / isomorphic (formal groups)). Let $F$ and $G$ be formal groups over $R$ given by power series $F$ and $G$.

• (i)
  A morphism $f:F\to G$ is a power series $f\in R[[T]]$ such that $f(0)=0$ satisfying

  $$f(F(X,Y))=G(f(x),f(Y)).$$

• (ii)
  $F\cong G$ if there exists $F\stackrel{f}{\to }G$ and $G\stackrel{g}{\to }F$ morphisms such that $f(g(X))=g(f(X))=X$.