This is an announcement for the paper "On multi-ideals and polynomial ideals of Banach spaces" by Daniel Pellegrino and Joilson Ribeiro. Abstract: The notion of coherent sequences of polynomial ideals and the notion of compatibility of a polynomial ideal with a given operator ideal were recently introduced by D. Carando, V. Dimant and S. Muro. These concepts play an important role in the theory of polynomial ideals, since they offer some properties that polynomial ideals must satisfy in order to keep the spirit of a given operator ideal and also maintain some coherence between the different levels of $n$-homogeneity. However, it seems to exist no reason to omit the multi-ideals from these cycle of ideas. In the present paper we revisit these notions; more precisely, we propose that these concepts are considered for a pair $(\mathcal{P}_{k},\mathcal{M}_{k})_{k=1}^{\infty}$, where $(\mathcal{P}% _{k})_{k=1}^{\infty}$ is a polynomial ideal and $(\mathcal{M}_{k}% )_{k=1}^{\infty}$ is a multi-ideal. The construction of our approach is inspired by the important special case of absolutely summing operators. Archive classification: math.FA Remarks: 16 pages Submitted from: dmpellegrino@gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1101.1992 or http://arXiv.org/abs/1101.1992