Poincaré/Koszul Duality for General Operads

Abstract: We record a result concerning the Koszul dual of the arity filtration on an operad. This result is then used to give conditions under which, for a general operad, the Poincar\'e/Koszul duality arrow of Ayala-Francis is an equivalence. We discuss how the Poincar\'e/Koszul duality arrow for the little $n$-disks operad $\mathcal{E}_n$ relates to their work when combined with the self-Koszul duality of $\mathcal{E}_n$.