In a previous work arXiv:0903.4512, we have built an homotopical Turaev-Viro
invariant and an HQFT from the universal graduation of a spherical category. In
the present paper, we show that every graduation $(G,p)$ of a spherical
category $\C$ defines an homotopical Turaev-Viro invariant $HTV_{\C}^{(G,p)}$
and an HQFT $\m{H}_{\C}^{(G,p)}$. Furthermore we show that the Turaev-Viro TQFT
will be split into blocks coming the HQFT $\m{H}_{\C}^{(G,p)}$.