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We consider partitions of a set with r elements ordered by refinement. We consider the simplicial complex Kˉ(r) formed by chains of partitions which starts at the smallest element and ends at the larg...
Koszul duality for Operads     Koszul duality  Operads       2015/3/25
This is a copy of the article by the same authors published in Duke Math. J. (1994).
A Koszul duality for props     Koszul duality  props       2015/3/25
The notion of prop models the operations with multiple inputs and multiple outpus, acting on some algebraic structures like the bialgebras or the Lie bialgebras. In this paper, we generalize the Koszu...
In this article we give a conceptual definition of Manin products in any category endowed with two coherent monoidal products. This construction can be applied to associative algebras, non-symmetric o...
Abstract: We give a proof of the parabolic/singular Koszul duality for the category O of affine Kac-Moody algebras. The main new tool is a relation between moment graphs and finite codimensional affin...
In this paper we prove a version of curved Koszul duality for Z/2Zgraded curved (dg) (co)algebras. A curved version of the homological perturbation lemma is also obtained as a useful technical tool fo...

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