A formal group law over a commutative ring $R$, (by [nLab](http://ncatlab.org/nlab/show/formal+group)) is a sequence of power srires 


$$
f\_1,...,f\_n\in R[[x\_1,...,x\_n,y\_1,...,y\_n]]
$$


such that, using the notation 


$$
x=(x\_1,...,x\_n),y=(y\_1,...,y\_n),f=(f\_1,...,f\_n)
$$


we have
$$
f(x,f(y,z))=f(f(x,y),z)
$$
$$
f(x,y)=x+y+\text{higher order terms}
$$


I understand vaguely the idea of a formal group law as a power series expansion of the group law of a lie group or an algebraic group (actual or hypothetical) in the neighborhood of the identity. But I would be happy to know, if only for psychological reasons, if this definition can be recovered as simply a group object in some category. 


In the [nLab](http://ncatlab.org/nlab/show/formal+group) entry about formal groups, it is written that formal group laws are one approach to formal groups, and the later is a group object in 'infinitesimal spaces', but I was unable to understand what is an infinitesimal space from the linked entry. I would appreciate if someone could explain this circle of ideas or point to the relevant literature.



Formal group law is a group object in ...?
A formal group law over a scheme $S$ is a group object in the category of framed formal schemes over $S$. Objects in this category are formal schemes $X$ over $S$ equipped with an $S$-isomorphism $X \to \operatorname{Spf} \mathscr{O}\_S[[t\_1,\ldots,t\_n]]$ for some $n$.


There is a functor from framed formal schemes over $S$ to formal schemes over $S$, given by forgetting the $S$-isomorphism. The essential image is the category of formal Lie varieties over $S$. This functor takes formal group laws to the class of formal groups that admit a framing.


