Hi! Does anyone know if there's a partial/concrete answer or literature about the following question: consider doing unstable homotopy theory over a Hopf operad H in positive char p, so we may e.g. consider the category of (unstable) commutative algebras in the category of left H-modules.
It is easy to see that this category is controlled by an operad which I will call Com_H, so it makes sense to consider the Andre--Quillen cohomology of these commutative H-algebras, since we're in particular taking commutative algebras we need to work with simplicial methods (like Turner--Goerss).