  The Kondo effect in a Tomonaga-Luttinger liquid ($U<<t$) is studied by using
the non-Abelian bosonization. The $q=2k_F$ enhanced spin fluctuations generate
a special Kondo effect, for any sign of the exchange coupling $J_K$
($\left|J_K\right|<<U$) with the impurity. Then, unlike in Fermi liquids ($U\to
0$), the presence of a $2k_F$-polarized screening cloud around the impurity
favors the occurrence of irrelevant electronic operators with scaling dimension
$d=3/2$: the thermodynamics is nearly this of the two-channel Kondo model in a
Fermi liquid. The Mott insulating transition does not affect much the ground
state, but rescales the power-law dependence of the Kondo temperature on $J_K$.
