  We study spontaneous symmetry breakings for fermions (spinless and spinful)
on a two-dimensional kagome lattice with nearest-neighbor repulsive
interactions in weak coupling limit, and focus in particular on topological
Mott insulator instability. It is found that at $\frac{1}{3}$-filling where
there is a quadratic band crossing at $\Gamma$-point, in agreement with Ref. 1,
the instabilities are infinitesimal and topological phases are dynamically
generated. At $\frac{2}{3}$-filling where there are two inequivalent Dirac
points, the instabilities are finite, and no topological phase is favored at
this filling without breaking the lattice translational symmetry. A
ferromagnetic quantum anomalous Hall state with infinitesimal instability is
further proposed at half-filling of the bottom flat band.
