Definition
Let \(\Gamma \to \omega\) be a be a family of tropical curves arising from graph data \((G, g, \ell)\). Said quickly, a family of tropical curves is the map \(h:\Gamma \to \Sigma(X)\) arising from tropicalizing a stable map \(f:(C/S)\to X\). Abstractly, they can be defined via a list of properties but this is the situation they’re defined to model.