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

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