4 problems

Let $\mathcal{X}$ be a quasi-compact fibered category over $R$, and let $\mathcal{C}$ be as in the resolution-property hypothesis of the paper. Write…

Eilenberg–Watts conjecture. The Eilenberg–Watts theorem should hold in any abelian monoidal category.

Let $\shE$ be a stable vector bundle of degree $0$ and rank $r$ on the projective space $\PP^N$. Its Tannaka dual group $G_{\shE}$ is a connected semisimple group whose almost simp…

Tannaka duality conjecture. The groupoid ${\mathcal T^{\infty}({\mathcal G})}$ is a Lie groupoid for every proper Lie groupoid ${\mathcal G}$, without assuming regularity.