Continuity of the tropical Prym-Torelli map

We give a new intrinsic construction of the continuous tropical Prym variety, originally due to Röhrle and Zakahrov. In particular, given a harmonic double cover of graphs we explicitly construct the tropical Prym as integral torus. Moreover, we show that the tropical Prym–Torelli map from the moduli space of harmonic double covers to the moduli space of principally polarised tropical abelian varieties is continuous.