Definition
We denote by \(\mathcal M(X/B,\beta)\) the stack of basic stable log maps of class \(\beta\). This is the category whose objects are basic stable logarithmic maps \((C/S, \mathbf p, f)\) of class \(\beta\) and whose morphisms \((C/S, \mathbf p, f) \to (C'/S',\mathbf p', f')\) are commutative diagrams
with the left-hand square cartesian, \(S\to S'\) strict and \(f = f'\circ g\), \(g\circ \mathbf p = \mathbf p' \circ h\).