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- W4299354018 abstract "We extend the bar-cobar adjunction to operads and properads, not necessarily augmented. Due to the default of augmentation, the objects of the dual category are endowed with a curvature. We handle the lack of augmentation by extending the category of coproperads to include objects endowed with a curvature. As usual, the bar-cobar construction gives a (large) cofibrant resolution for any properad, such as the properad encoding unital and counital Frobenius algebras, a notion which appears in 2d-TQFT. We also define a curved Koszul duality theory for operads or properads presented with quadratic, linear and constant relations, which provides the possibility for smaller relations. We apply this new theory to study the homotopy theory and the cohomology theory of unital associative algebras." @default.
- W4299354018 created "2022-10-02" @default.
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- W4299354018 date "2010-08-31" @default.
- W4299354018 modified "2023-09-26" @default.
- W4299354018 title "Curved Koszul duality theory" @default.
- W4299354018 doi "https://doi.org/10.48550/arxiv.1008.5368" @default.
- W4299354018 hasPublicationYear "2010" @default.
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