Suppose we have maps A←B→C of symmetric monoidal ∞-categories where B→A is strong symmetric monoidal, B→C is lax symmetric monoidal. If we take the pushout in symmetric monoidal ∞-categories with lax symmetric monoidal functors between them, is there a way to naturally equip the map C→P (where P is the pushout) with a strong symmetric monoidal structure in some universal way?
