Let $K$ be a field. For any differentially graded coalgebra $A$ over $K$, any differentially graded right $A$-comodule $M$ over $K$ and any differentially graded left $A$-comodule $N$ over $K$ let
$\mathrm{Cotor}_A(M,N)$ denote the cotorsion product of $M$ and $N$ relative to $A$.

The graded $K$-vector space $\mathrm{Cotor}_A(M, \, N)$ is by definition the homology of the totalization of the cosimplicial cochain complex over $K$ with $n$-th term $M \otimes A^{\otimes n} \otimes N$,
where the tensor product is in cochain complexes over $K.$

Let $X \to Y$ be a Serre fibration between connected spaces and $F$ its fiber over a given point $y$ of $Y.$ If $Y$ is simply connected, by a theorem of Eilenberg and Moore there is a canonical isomorphism
\begin{equation}
H_*(F;K)\cong \mathrm{Cotor}_{C_*(Y; \, K)}(C_*(X; \, K), \, C_*(*; \, K)), \ \ \ \ (**)
\end{equation}
where $C_*(-;\, K)$ are singular chains with coefficients in the field $K.$

> **Question.** Can we replace the condition that $Y$ is simply connected by a weaker condition? For example, is there still a
> canonical isomorphism $(**)$ if $$Y = BG = K(G,\, 1)$$ for $G$ a
> derived $p$-complete abelian group?