(2.1.5) Let $h:\mathscr{Y}\to\mathscr{X}$ be a proper morphism of normal $\mathscr{C}$-models of $X$. Assume that $K_{\mathscr{X}}+(\mathscr{X}_{s})_{\mathrm{red}}$ is $\mathbb{Q}$-Cartier. Then the log pullback of $(\mathscr{X}_{s})_{\mathrm{red}}$ to $\mathscr{Y}$ is the unique $\mathbb{Q}$-Weil divisor $\Delta$ on $\mathscr{Y}$ such that $K_{\mathscr{Y}}+\Delta$ is $\mathbb{Q}$-linearly equivalent to

$$f^{*}(K_{\mathscr{X}}+(\mathscr{X}_{s})_{\mathrm{red}})$$

and $f_{*}\Delta=(\mathscr{X}_{s})_{\mathrm{red}}$.