A Koszul duality for props

Bruno Vallette (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

The notion of prop models the operations with multiple inputs and multiple outputs, 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.

Keywords: Operads; Props; Properads; Koszul duality

Domains: K-Theory and Homology [math.KT]; Quantum Algebra [math.QA]

Bruno Vallette. A Koszul duality for props. Transactions of the American Mathematical Society, 2007, 359 (10), pp.4865-4943. ⟨10.1090/S0002-9947-07-04182-7⟩. ⟨hal-00581048⟩