Francesca Pratali

collaborators

5 papers

math.AT2026

Relative dendroidal Rezk nerve and applications

Kensuke Arakawa, Victor Carmona, Francesca Pratali

We extend the dendroidal Rezk nerve to the setting of relative $\infty$ -operads. Our main theorem relates it to localization of $\infty$ -operads, generalizing a theorem of Mazel-Ge…

math.AT2026

The root functor

Francesca Pratali

In this paper, we show that any $\infty$ -operad is equivalent to the localization of a discrete $I^£$ -free operad; this result extends Joyal's delocalization theorem for categories…

math.AT2025

Relative operads model $\infty$ -operads

Kensuke Arakawa, Victor Carmona, Francesca Pratali

Given a (colored) operad and a set of unary operations, we can form an associated $\infty$ -operad via localization. We show that localization determines an equivalence of homotopy…

math.AT2025

Rectification of dendroidal left fibrations

Francesca Pratali

For a discrete colored operad $P$ , we construct an adjunction between the category of dendroidal sets over the nerve of $P$ and the category of simplicial $P$ -algebras, and prove t…

math.AT2025

A straightening-unstraightening equivalence for $\infty$ -operads

Francesca Pratali

We provide a straightening-unstraightening adjunction for $\infty$ -operads in Lurie's formalism, and show it establishes an equivalence between the $\infty$ -category of operadic le…

Relative dendroidal Rezk nerve and applications

The root functor

Relative operads model ∞-operads

Rectification of dendroidal left fibrations

A straightening-unstraightening equivalence for ∞-operads

Relative operads model $\infty$ -operads

A straightening-unstraightening equivalence for $\infty$ -operads