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For $N_\infty$ operads $\mathcal O$ and $\mathcal O'$ such that there is aninclusion of the associated indexing systems, there is a forgetful functor fromincomplete Tambara functors over $\mathcal O'$ to incomplete Tambara functorsover $\mathcal O$. Roughly speaking, this functor forgets the norms in$\mathcal O'$ that are not present in $\mathcal O$. The forgetful functor hasboth a left and a right adjoint; the left adjoint is an operadic tensorproduct, but the right adjoint is more mysterious. We explicitly compute theright adjoint for finite cyclic groups of prime order.

The right adjoint to the equivariant operadic forgetful functor on incomplete Tambara functors