Homomorphism of formal group laws

Definition
Suppose $$F$$ and $$G$$ are defining ingredient::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 $$y = (y_1,y_2,\dots,y_m)$$.

Related notions

 * Isomorphism of formal group laws is a homomorphism of formal group laws that has an inverse that is also a homomorphism. If an isomorphism exists between two formal group laws, then they must have the same dimension.
 * Strict isomorphism of formal group laws is an isomorphism $$\varphi$$ of formal group laws such that $$\varphi(x) - x$$ has terms of degree two and higher only.