ScalingStacks

Proposition 3.10. Let $f:X\rightarrow Y$ be a perfect morphism. Then $f_{*}:\qc(X)\to\qc(Y)$ commutes with all small colimits and satisfies the projection formula. Furthermore, if $g:Y^{\prime}\rightarrow Y$ is any map of derived stacks, the resulting base change map $g^{*}f_{*}\rightarrow f^{\prime}_{*}g^{\prime*}$ is an equivalence.