2-coherence of the smash-product functor

Prove that, in Book HoTT, the smash-product functor X ∧ − : U∗ → U∗ is 2-coherent for every pointed type X.

Background

The paper proves 2-coherence for the suspension functor and extends the method to the join functor. The smash product is another construction that generalizes suspension, so establishing its 2-coherence would provide a further application of the paper’s coherence framework.

The authors explain that the usual homogeneous-type argument does not apply directly because the right adjoint of the smash product is the pointed map-space functor, which is not generally valued in homogeneous types. Thus a different technique is needed to resolve the required higher equality in Book HoTT.