Abstract We study tetrahedron maps, which are set-theoretical solutions to the Zamolodchikov equation, and Yang–Baxter quantum equation. In particular, we clarify structure of nonlinear algebraic relations define linear (parametric) maps (with dependence on parameters), present several transformations allow one obtain new such from known ones. Furthermore, prove that differential a (nonlinear) ...

In this note, we attack a question posed ten years ago by Tsukiyama about the injectivity of the socalled Forgetable map. We show that we can insert the Forgetable map in an exact sequence and that the problem can be reduced to the computation of the sequence which turns out unexpectedly to be related to the phantom map problem and the famous Halperin conjecture in rational homotopy theory.