9 problems

Let $d$ be a nonnegative integer, and let ${\mathsf{OEpi}}_{\leq d}$ be the category of finite-dimensional inner product spaces of dimension at most $d$ and orthogonal epimorphisms…

Let $\Gmr$ be a finite group and let $\upalpha$ be an indexing representation. Let $\Ecal_{\Gmr, {\bf 0}}^{\Sigma, {\sf conn}}$ be the category of connected-at-infinity equivariant…

Let $\Gmr$ be a finite group, and let ${\bf B}_{\Gmr}{\bf Top}^{(1)}$ denote the first layer of the equivariant Weiss functor ${\bf B}_{\Gmr}{\bf Top}$. Suppose there exists an inc…

Behrens's conjecture. The transforms defined using these characters, with values in right modules over $\mathsf{OEpi}$, should play an important role in Weiss calculus.

Arone's conjecture. The category formed by these sections is equivalent to $K(\mathsf{OEpi})$. Moreover, $\mathsf{OEpi}$ is a twisted Koszul self-dual category: $K(\mathsf{OEpi})$…

Bimodule chain-rule conjecture. For functors

Mixed chain-rule conjecture. There is an equivalence of right $K(\mathsf{OEpi})$-modules

Product-rule conjecture. There is an equivalence of right $K(\mathsf{OEpi})$-modules

Symmetric monoidality conjecture. For $\mathsf{OEpi}$,