arXiv subjects

Aowen Fan

Publications and source records attributed to Aowen Fan.

2 recordsLinked to original sources

arXiv2026

Infinity operad pairs, higher distributivity and spectral Tambara functors

We introduce an $\infty$-categorical model of operad pairs and their associated bimonoidal categories. We study the related concepts such as cocartesian-cartesian operad pairs, algebra pairs and the Day convolution. Using the Day convolution for operad pairs, we can define distributive functors between a symmetric bimonoidal category and a cartesian closed monoidal category. As an application, we show that for a finite group $G$, the operadic distributive functors from $\mathrm{Span}(\mathsf{Fin}_G)$ to any cartesian closed monoidal category coincides with the distributive functors defined by the distributive diagram. Therefore, we show that the connective $G$-equivariant $\mathbb{E}_{\infty}$-ring spectra are equivalently the spectral $G$-Tambara functors.

math.AT↗

arXiv2026

On the Kelly monoidal structure of $Λ$-sequences and unital operads

Let $Λ$ be the category of based finite sets $\mathbf{n}$ and based injections. We study properties of monoids and modules in $Λ$-sequences under the Kelly monoidal structure. In particular, we show that the forgetful functor from right modules in $Λ$-sequences to right modules in symmetric sequences is an isomorphism. We show that any compatible lower data extends to a normal oplax monoidal structure and use this to establish a universal normal oplax monoidal structure on $Λ$-sequences extending the Kelly product, identifying unital operads to monoids in unital $Λ$-sequences for a general symmetric monoidal category $\mathscr{V}$. We also establish a closed monoidal localization theorem.

math.AT↗