🌀Preprints (available on arXiv)
The root functor  [arXiv: 2505.14288] submitted
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.
Rectification of dendroidal left fibrations [arXiv: 2502.17415] submitted
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.
A straightening-unstraightening for oo-operads [arXiv:2501.05263] submitted
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] submitted
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.