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Koszul duality between En-algebras and coalgebras in a filtered category

2014/09/24 by Matsuoka, Takuo
#13B35 #16W70 #18D10 #18E30 #18G55 #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT) #Primary: 16E40 #Secondary: 16D90

paper · doi:10.48550/arxiv.1409.6943

Abstract

We study the Koszul duality between augmented En-algebras and augmented En-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.

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