ScalingStacks

If \(\mathcal O\) is a small operad, \(I\) is \(\mathcal O\)-monoidal, \(\mathcal C\) is presentably \(\mathcal O\)-monoidal and \((\mathcal L, \mathcal R)\) is compatible with the \(\mathcal O\)-monoidal structure on \(\mathcal C\), then \((\mathcal L^I, \mathcal R^I)\) is compatible with the Day convolution \(\mathcal O\)-monoidal structure on \(\mathrm{Fun}(I, \mathcal C)\).