🌀Pubblications and accepted pubblications
Rectification of dendroidal left fibrations [arXiv: 2502.17415] to appear in Algebraic and Geometric Topology. Final version here
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 that when P is Σ-free it establishes a Quillen equivalence with respect to the covariant model structure on the former category and the projective model structure on the latter.
🌀Preprints (available on arXiv. Here the most up to date versions)
Relative dendroidal Rezk nerve and applications [arXiv:2606.11895] with K. Arakawa and V. Carmona, sumbitted
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 Aaron Mazel-Gee. This provides a powerful tool for operadic localization, leading to new results on cyclic operads, operadic modules, and factorization algebras on spheres.
Relative operads model oo-operads, [arXiv:2505.14288] with K. Arakawa and V. Carmona, sumbitted
We build up on the root functor and show that localization induces an equivalence of homotopy theories between relative operads and oo-operads. As an application we show that Lurie's nerve functor induces an equivalence of oo-categories.
The root functor [arXiv: 2505.14288] sumbitted
We prove that any oo-operad is the localization of a discrete one by constructing the discrete resolution in the dendroidal formalism. We prove that operadic localization is compatible with the projective and covariant model structures and deduce the characterization of the oo-category of algebras over an oo-operad as locally constant algebras over its discrete resolution.
A straightening-unstraightening for oo-operads [arXiv:2501.05263] sumbitted
We provide a straightening-unstraightening adjunction for oo-operads in Lurie's formalism, and show it establishes an equivalence between the oo-category of operadic left fibrations over an oo-operad O and the oo-category of O-algebra in spaces.
Higher structures on homology groups, with N. Kowalzig [arXiv:2406.06710]
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 with comultiplication induces a homology theory that is endowed with the structure of a Gerstenhaber coalgebra.