Gregoire Marc | Searcharxiv

arXiv2026

On sifted homotopy colimits of algebras over an $N_{\infty}$-operad

We prove that the forgetful functor from algebras over an $N_{\infty}$-operad to equivariant spaces preserves sifted homotopy colimits

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arXiv2025

Homotopy theory of simplicial parametrized operads

We define a generalization of (coloured) operads based on double lax functors and we construct a model structure on the associated category of generalized simplicial (coloured) operads. In particular, we obtain a model structure on the category of simplicial (coloured) O-operads of Nardin and Shah.

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arXiv2024

A higher Mackey functor description of algebras over an $N_{\infty}$-operad

Suppose $G$ is a finite group. In this paper, we construct an equivalence between the $\infty$-category of algebras over an $N_{\infty}$-operad $\mathcal{O}$ associated to a $G$-indexing system $\mathcal{I}$ and the corresponding $\infty$-category of higher incomplete $\mathcal{I}$-Mackey functors with value in spaces. We use the universal property of the incomplete $(2, 1)$-category of spans of finite $G$-sets $\mathscr{A}_{\mathcal{I}}$ to construct a functor from $\mathscr{A}_{\mathcal{I}}$ to the $2$-category of $\mathcal{I}$-normed symmetric monoidal categories of Rubin. We then show that the left Kan extension of the composition of this functor with the core functor along the Yoneda embedding is an equivalence.

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