@ArunDebray Well so I'm less sure of all of this now, but yeah, it would be valued in vector spaces most likely, but I don't really know, I was just kind of fiddling around.

And ofc the ultimate goal is to have things valued in Top or Sp and to get topological enhancements similar to the homotopy types that give Khovanov homology.

Does anyone know of any papers or notes that actually go into the details of calculating the Moore normalization of some simplicial abelian group? I'm dealing with a few homology spectral sequences associated to simplicial spaces, and I'm trying to see if I can get some nicer descriptions of the second pages by describing this normalization. Some of the more complex cases are trying to describe the Moore normalization of the simplicial replacement of some simplicial abelian group.