The Stacks project

Definition 71.6.10. Let $S$ be a scheme. Let $f : X' \to X$ be a morphism of algebraic spaces over $S$. Let $D \subset X$ be an effective Cartier divisor. We say the pullback of $D$ by $f$ is defined if the closed subspace $f^{-1}(D) \subset X'$ is an effective Cartier divisor. In this case we denote it either $f^*D$ or $f^{-1}(D)$ and we call it the pullback of the effective Cartier divisor.