  The recently discovered material Co$_3$Sn$_2$S$_2$ shows an impressive
behavior of the quantum anomalous Hall (QAH) conductivity driven by the
interplay between ferromagnetism in the $z$ direction and antiferromagnetism in
the $xy$ plane. Motivated by these facts, first we build and study a spin-1/2
model to describe the magnetism of Co-atoms on the Kagome planes. Then, we
include conduction electrons which are coupled to the spins-1/2 through a
strong Hund's coupling. The spin-orbit coupling results in topological
low-energy bands. For 2/3 on-site occupancy, we find a topological transition
from a QAH ferromagnetic insulating phase with Chern number one to a quantum
spin Hall (QSH) antiferromagnetic phase. The QAH phase is metallic when
slightly changing the on-site occupancy. To account for temperature effects, we
include fluctuations in the direction of the Hund's coupling. We show how the
Hall conductivity can now smoothly evolve when spins develop a $120^o$
antiferromagnetism in the $xy$ plane and can synchronize with the ferromagnetic
fraction.
