Let $X$ and $Y$ be complex manifolds, let $F: X \to Y$ be a holomorphic map, and let $p,q \in \mathbb{N} \cup \{0\}$. If $\alpha \in A^{p,q}(Y)$ is a smooth complex-valued differential form of type $(p,q)$ on $Y$, then its pullback $F^*\alpha$ is a smooth complex-valued differential form of type $(p,q)$ on $X$; that is, $F^*\alpha \in A^{p,q}(X)$.