  The category of topological spaces endowed with two marked points is equipped
with two families $\mathbf F_n$ and $\mathbf H_n$ of functors to the category
of abelian groups, indexed by a nonnegative integer $n$: namely, the functor
$\mathbf F_n$ takes the object $(X,x,y)$ to the quotient of $\mathbb
Z\pi_1(X,x,y)$ by an abelian subgroup associated with the $n+1$-st power of the
augmentation ideal of the group algebra $\mathbb Z\pi_1(X,x)$, and the functor
$\mathbf H_n$ takes the same object to the $n$-th singular homology group of
$X^n$ relative to a subspace defined in terms of partial diagonals. We
construct a family of natural transformations $\nu_n : \mathbf F_n\to \mathbf
H_n$. We identify the natural transformation obtained by restricting $\nu_n$ to
the subcategory of algebraic varieties with a natural equivalence due to
Beilinson.
