functional dependence ${\cal O}$ $$\label{transf2}
 R\left[{\cal O}\left(\{{\sigma}_l\}, {\bf K}\right)\right]
  \,=\,{\cal O}\left(\{{\mu}_m\}, {\bf K}'\right)\;.$$ By further mathematical analysis of a particular RGT $R$ defined by (\[transf2\]) this hopefully yields to a dependence of the [*renormalized*]{} parameters ${\bf K}'$ on the old parameters ${\bf K}$ which is called the [*flow behaviour*]{} of the RGT. We like to emphasize that once the functional dependence ${\cal O}\left(\{{\sigma}_l\}, {\bf K}\right)$ is known, we immediately know the functional dependence ${\cal O}\left(\{{\mu}_m\}, {\bf K}'\right)$ which plays an important role in our construction.\
We now make the Ansatz that in principle each RGT $R$ can be written as a composition of two maps, called [*embedding*]{} and [*truncation*]{} [@gmdsv95]. This terminology originates from a RG technique for Hamiltonian systems [@jpfd78], which was then further developed and used for calculations of the flow behaviour [@gmdsv95]. Rephrasing equation (\[transf2\]) and focusing only on the renormalization of the set of parameters for determining the flow behaviour we get $$\label{transf4}
 G^+\,\circ\,{\cal O}\left({\bf K}\right)\,\circ\, G
  \,=\,{\cal O}\left({\bf K}'\right)$$ where we denote $G^+$ as the [*truncation map*]{} and $G$ as the [*embedding map*]{}.\
As a quite intuitive example for the abstract definition of the operators $G^+$ and $G$, in the special case of a functional 