On the periodic v2–self-map of A1

The spectrum Y := M-2(1) boolean AND C eta admits eight v(1)-self-maps of periodicity 1. These eight self-maps admit four different cofibers, which we denote by A(1)[i j] for i, j is an element of {0, 1}. We show that each of these four spectra admits a v(2)-self-map of periodicity 32.