4 problems

Let $\mathbf{D}\subset\mathbf{T}$ be a pseudo-tensor subcategory of a tensor category. It is strongly generating if every object in $\mathbf{T}$ is a quotient of an object in…

Let $\mathbf{D}$ be a pseudo-tensor category embedded in a tensor category $\mathbf{T}$. Say that the embedding has the quotient property if every object in $\mathbf{T}$ is a quoti…

Let $\mathbf{D}$ be a pseudo-tensor category and let $\mathbf{T}$ be a tensor category containing it through an abelian envelope. The quotient property means that every object of…

Let $p=2$, and consider the limit of finite symmetric tensor categories referred to by Benson and Etingof. Benson–Etingof conjecture. This limit is tensor equivalent to the categor…