A formal group law over a commutative ring $R$, (by nLab) 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 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.