8 problems

Let $B$ be a Noetherian algebra, and let $N$ be a Wedderburn projective $B$-module. Write $\tau_N(B)$ for the trace of $N$ in $B$. Wedderburn-projective Idempotent Nakayama Conject…

Let $(C,e)$ be a Wedderburn context, with $C$ a Noetherian algebra, and let $\overline{C}=C/CeC$ be its Morita defect. Idempotent Nakayama Conjecture. If … then $\overline{C}=0$. E…

Opper's Morita invariance conjecture. Under the additional assumptions on $\mathcal{C}$ needed for $\operatorname{Aut}^{\infty}_{\circ}(\mathcal{C})$ to describe the identity compo…

Let $\mathcal{E}$ be a finite symmetric tensor category. Let $\mathrm{Mor}_2^{\mathrm{fin}}(\mathbf{Pr}_{\mathcal{E}})$ be the symmetric monoidal sub-4-category whose objects are f…

Let $\mathcal{C}$ be a graded $\Bbbk$-linear category such that … for all $C,D\in\operatorname{Ob}(\mathcal{C})$ and all $i\geq 1$. Write…

Let $\mathbf{Vec}$ denote the category of finite-dimensional vector spaces over a field $\mathbb K$. The object $\Sigma^2\mathbf{Vec}$ is the twofold delooping associated to vector…

Let $\mathcal{C}$ be a fully dualizable object, and let $Z(\mathcal{C})=HH^\bullet(\mathcal{C})$ denote its Hochschild cohomology. Consider a category of fully dualizable objects a…

Let $A$ be a nonunital ring. It is h-unital when the relevant Tor groups vanish, namely … for every integer $n\geq 0$, where $\widetilde{A}$ denotes the unitalization of $A$. Quill…