Homomorphism of formal group laws

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Suppose F and G are formal group laws of dimensions m and n respectively. A homomorphism from F to G is a collection \varphi = (\varphi_1,\varphi_2,\dots,\varphi_n) of n power series in m variables such that the following holds formally:

G(\varphi(x),\varphi(y)) = \varphi(F(x),F(y))

where x = (x_1,x_2,\dots,x_m) and y = (y_1,y_2,\dots,y_m).

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