A Koszul duality for props

Abstract

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 Koszul duality theory of associative algebras and operads to props.

Last version before publication in Transactions of the A.M.S (statement about the properad of involutive Lie bialgebras removed)

References in corpus (8)

• Homology of generalized partition posets
• Combinatorial operad actions on cochains
• Koszul duality of operads and homology of partition posets
• PROP profile of deformation quantization and graph complexes with loops and wheels
• Free monoid in monoidal abelian categories
• Dualite de Koszul des PROPs
• PROPped up graph cohomology
• A resolution (minimal model) of the PROP for bialgebras

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