Koszul dual $\mathcal{A}_{\infty}$-algebras from star-shaped diagrams -- part 2

This paper proves a Koszul duality result between weighted $\mathcal{A}_{\infty}$-algebras constructed in the author's previous work. In the process, we construct a new box tensor product for weighted $\mathcal{A}_{\infty}$ bimodules, and verify a correspondence between weighted $\mathcal{A}_{\infty}$-algebra maps and a particular class of $\mathcal{A}_{\infty}$-bimodule. This paper is part 2 of arXiv:2408.01564.