6 papers
Relative dendroidal Rezk nerve and applications
Kensuke Arakawa, Victor Carmona, Francesca Pratali
We extend the dendroidal Rezk nerve to the setting of relative -operads. Our main theorem relates it to localization of -operads, generalizing a theorem of Mazel-Ge…
Relative operads model -operads
Kensuke Arakawa, Victor Carmona, Francesca Pratali
Given a (colored) operad and a set of unary operations, we can form an associated -operad via localization. We show that localization determines an equivalence of homotopy…
The root functor
Francesca Pratali
In this paper, we show that any -operad is equivalent to the localization of a discrete -free operad; this result extends Joyal's delocalization theorem for categories t…
Rectification of dendroidal left fibrations
Francesca Pratali
For a discrete colored operad , we construct an adjunction between the category of dendroidal sets over the nerve of and the category of simplicial -algebras, and prove t…
A straightening-unstraightening equivalence for -operads
Francesca Pratali
We provide a straightening-unstraightening adjunction for -operads in Lurie's formalism, and show it establishes an equivalence between the -category of operadic le…
Higher structures on homology groups
Niels Kowalzig, Francesca Pratali
We dualise the classical fact that an operad with multiplication leads to cohomology groups which form a Gerstenhaber algebra to the context of cooperads: as a result, a cooperad w…