Koszul duality between $E_n$-algebras and coalgebras in a filtered category

Abstract

We study the Koszul duality between augmented $E_n$-algebras and augmented $E_n$-coalgebras in a symmetric monoidal stable infinity $1$-category equipped with a filtration in a suitable sense. We obtain that the Koszul duality constructions restrict to an equivalence between augmented algebras and coalgebras which have some positivity and completeness with respect to the filtration. We also obtain that the Koszul duality construction is functorial between carefully constructed generalized Morita categories consisting of those algebras/coalgebras in each dimension.

Was previously part of arXiv:1312.2562. 35 pages. Technical improvements, more descriptive terminology

References in corpus (3)

• Higher Topos Theory
• Supersymmetric gauge theory and the Yangian
• Koszul duality for locally constant factorization algebras

Cited by in corpus (1)

• Koszul duality for locally constant factorization algebras