There is only one node, %$t$% at the top level, %$\alpha $%, of the tree, which is therefore full, and so an object %${\mathcal O}$% is homogeneous at level %$\alpha $% just if %${\mathcal O}_{t}={\mathcal O}_{t}f_{tt}$%. But %$f_{tt}$% is the identity function.