let me clarify, $\mathbb{G}_a(R)=R$. I'd like some kind of.... deformation of $\mathbb{G}_a$, call it $\mathbb{G}_a'$ such that $\mathbb{G}_a'(R)=R[x]/(x^n)$
if you have a representable functor valued in cogroups you are looking at a cogroup object in the category not a group object even though the functor is contravariant
yeah, all i do is sit in this chatroom and eat cheezits
@davidroberts the short of it is, i'm trying to think about building formal group laws up from what are called n-buds, or formal group law k-chunks, from a deformation theory perspective
and i guess i'd like to think about it as something like.... deforming cogroup structures on a certain scheme
yeah. i'm sort of pleased with it. Michel Lazard basically proved that any n-bud can be deformed into an n+1-bud, but he didn't do it from this perspective
there are papers by charles rezk and a student of tyler lawson which give explicit models for the honda formal group laws in characteristics 2 and 3 and at height 2 using accidentally available models of elliptic curves