In this talk, we use the fact that categories with a fixed object set are the monoid objects in a category of “graphs” to develop a formalism for defining the Koszul dual in this context. We then explain its relationship with the theory of Koszul duality for operads in spaces and spectra developed by Michael Ching, through the functor associating to an operad P the corresponding prop, which is a category with the natural numbers as object set. We also mention potential applications.

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