@AlexanderCampbell okay yeah that's what I thought. Looking at the definition of "simplicial model category" I think this follows from the "pullback powering" condition, using the cofibration $\ast\to X$ and the fibration $A\to B$.
Is there a definition of a level structure on a formal group that does not involve asking for divisibility of power series (as in, arxiv.org/abs/1010.4241), which I find slightly opaque? Where can I find it?
(Or at least a discussion of this condition that would help me understand it? For example, I find the definition in the elliptic case given in Lurie's paper on level structures on elliptic curves slightly easier to digest.)
As a second question, as I understand it, if I attach to $\mathbb{Q}_{p}$ the $p$-th roots of the Lubin-Tate formal group (which is height $1$ over the special fibre), I will obtain the ramified part of the maximal abelian extension of $\mathbb{Q}_{p}$, whose Galois group I can write down explicitly. What would happen if instead I attached $p$-roots of a formal group which is of height $h > 1$ over the special fibre?
