Homology, Homotopy and Applications

Volume 24 (2022)

Number 2

Poincaré/Koszul duality for general operads

Pages: 1 – 30

DOI: https://dx.doi.org/10.4310/HHA.2022.v24.n2.a1


Araminta Amabel (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.)


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 Poincaré/Koszul duality arrow of Ayala and Francis is an equivalence, using a proof similar to theirs. We discuss how the Poincaré/Koszul duality arrow for the little disks operad $\mathcal{E}_n$ relates to the work of Ayala and Francis when combined with the self-Koszul duality of $\mathcal{E}_n$.


operad, Koszul duality, Goodwillie calculus, factorization homology

2010 Mathematics Subject Classification


The author was supported by NSF Grant No. 1122374 while completing this work.

Received 25 March 2021

Received revised 7 August 2021

Accepted 7 August 2021

Published 10 August 2022