Koszul duality between $E_n$-algebras and coalgebras in a filtered category
Algebraic Topology
2018-03-20 v4 K-Theory and Homology
Abstract
We study the Koszul duality between augmented -algebras and augmented -coalgebras in a symmetric monoidal stable infinity -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.
Keywords
Cite
@article{arxiv.1409.6943,
title = {Koszul duality between $E_n$-algebras and coalgebras in a filtered category},
author = {Takuo Matsuoka},
journal= {arXiv preprint arXiv:1409.6943},
year = {2018}
}
Comments
Was previously part of arXiv:1312.2562. 35 pages. Technical improvements, more descriptive terminology