Koszul duality for dioperads

Wee Liang Gan

Koszul duality for dioperads

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arxiv math/0201074 v2 pith:3UDVEOVH submitted 2002-01-10 math.QA

Wee Liang Gan This is my paper · ORCID

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keywords koszuldioperaddioperadsdualitymultiplebialgebracertaindescribe

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We introduce the notion of a dioperad to describe certain operations with multiple inputs and multiple outputs. The framework of Koszul duality for operads is generalized to dioperads. We show that the Lie bialgebra dioperad is Koszul.

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Graded Frobenius Algebras
math.AT 2024-12 accept novelty 6.0 of 10

Graded Frobenius algebras are defined via a graph-based PROP, and an equivalence with explicit map-and-relation descriptions, including all required signs, is proved.

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