A perfect pairing for monoidal adjunctions

TL;DR

This paper provides a new proof of the duality between certain monoidal ∞-categories using a perfect pairing, enhancing understanding of their adjunction relationships.

Contribution

It introduces a novel proof technique for the dual equivalence of monoidal ∞-categories via a perfect pairing construction.

Findings

Establishes a dual equivalence between monoidal ∞-categories with specific functors.

Constructs a perfect pairing that demonstrates the duality.

Provides an alternative proof method for the duality result.

Abstract

We give another proof of the fact that there is a dual equivalence between the $\infty$-category of monoidal $\infty$-categories with left adjoint oplax monoidal functors and that with right adjoint lax monoidal functors by constructing a perfect pairing between them.