Geodesic
Modular operads as modules over the Brauer properad
Theory and applications of categories, Tome 38 (2022), pp. 1538-1607.

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We show that modular operads are equivalent to modules over a certain simple properad which we call the Brauer properad. Furthermore, we show that, in this setting, the Feynman transform corresponds to the cobar construction for modules of this kind. To make this precise, we extend the machinery of the bar and cobar constructions relative to a twisting morphism to modules over a general properad. This generalizes the classical case of algebras over an operad and might be of independent interest. As an application, we sketch a Koszul duality theory for modular operads.
Publié le :
Classification : 18M85, 18M70
Keywords: Modular operads, properads, Koszul duality 
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     author = {Robin Stoll},
     title = {Modular operads as modules over the {Brauer} properad},
     journal = {Theory and applications of categories},
     pages = {1538--1607},
     publisher = {mathdoc},
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     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2022_38_a39/}
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Robin Stoll. Modular operads as modules over the Brauer properad. Theory and applications of categories, Tome 38 (2022), pp. 1538-1607. http://geodesic.mathdoc.fr/item/TAC_2022_38_a39/