7 problems

Extremely strong Artinian conjecture, second version. For every $n\in\mathbb{N}$, the functor $\omega_n$ induces an equivalence

Extremely strong Artinian conjecture, first version. For every $n\in\mathbb{N}$, the functor $\omega_n$ induces an equivalence

Omega-adapted nilpotence conjecture. An object of finite type in $\mathcal{F}$ is omega-adapted of height at most $n-1$ if and only if it is $\tilde{\nabla}_n$-nilpotent.

Extremely strong Artinian conjecture. For every $n\in\mathbb{N}$, the subcategory $\mathcal{F}^{\omega-ad(n)}$ is stable under quotients.

Noetherian nilpotence conjecture. An object of finite type in $\mathcal{F}$ is noetherian of type $n-1$ if and only if it is $\tilde{\nabla}_n$-nilpotent.

Let $\mathcal{F}_{\mathcal{G}r,n}$ be the category of Grassmannian functors of level $n$, let $\omega_n$ be the exact functor to $\mathcal{F}$, and let $G^f_0$ denote the Grothendi…

Let $\mathcal{F}_{\mathcal{G}r,n}$ be the category of Grassmannian functors of level $n$, let $\mathcal{F}^{lf}_{\mathcal{G}r,n}$ be its full subcategory of locally finite objects,…