Application of waist inequality to entropy and mean dimension: II

Let $X$ be the full-shift on the alphabet $[0, 1]^a$ and let $(Y, S)$ be an arbitrary dynamical system. We prove that every equivariant continuous map from $X$ to $Y$ has conditional metric mean dimension at least $a-{\rm mdim}(Y, S)$. This solves a problem posed in part I of this paper (2023), co-authored with Ruxi Shi.