  A connection between the Galois-theoretic approach to semi-abelian homology
and the homological closure operators is established. In particular, a
generalised Hopf formula for homology is obtained, allowing the choice of a new
kind of functors as coefficients. This makes it possible to calculate the
fundamental groups corresponding to many interesting reflections arising, for
instance, in the categories of groups, rings, compact groups and simplicial
loops.
