  Based on the study of non-invertible symmetries, we propose there exist
infinitely many new renormalization group flows between Virasoro minimal models
$\mathcal{M}(kq + I, q) \to\mathcal{M}(kq-I, q)$ induced by $\phi_{(1,2k+1)}$.
They vastly generalize the previously proposed ones $k=I=1$ by Zamolodchikov,
$k=1, I>1$ by Ahn and L\"assig, and $k=2$ by Dorey et al. All the other
$\mathbb{Z}_2$ preserving renormalization group flows sporadically known in the
literature (e.g. $\mathcal{M}(10,3) \to \mathcal{M}(8,3)$ studied by Klebanov
et al) fall into our proposal (e.g. $k=3, I=1$). We claim our new flows give a
complete understanding of the renormalization group flows between Virasoro
minimal models that preserve a modular tensor category with the $SU(2)_{q-2}$
fusion ring.
