Let $f: X \to Y$ be a morphism of schemes, $\mathcal{G}$ be an $\mathcal{O}_Y$-module. Then we define the tensor product of $f^{-1}\mathcal{O}_Y$ -modules $f^*\mathcal{G} := f^{-1}\mathcal{G}\otimes_{f^{-1}\mathcal{O}_Y}\mathcal{O}_X$.
In Qing Liu's Algebraic Geometry and Arithmetic Curves, he said that $f^*$ commutes with taking direct sums (in the proof of Proposition 1.14 (Page 163)), but I don't know why this holds.
I know that $f^*$ is right exact hence commutes with finite colimits. But what will happen when we consider infinite direct sums? And I don't know how to prove it directly since we will take the sheafification in constructing the tensor product and direct sum.
Both $f^{-1}$ and tensor product commute with direct sums, hence so does $f^*$.