\node (open) at (0, 2) {$\sqcap^{n,i,\varepsilon}$};
\node (box) at (0, 0) {$\square^n$};
\node (set) at (2, 0) {$X$};

\draw[right hook->] (open) -- (box);
\draw[->] (open) -- node[midway] {f} (set);
\draw[dotted, ->] (box) -- node[midway, below] {g} (set);