3 problems

Let $\Omega$ be an arbitrary quiver, not necessarily eventually outward, and let $\operatorname{rep}(\Omega)$ denote the category of locally finite-dimensional representations of…

Removal of the eventually outward condition. In the category $\operatorname{Rep}_{\mathrm{lf}}(\Omega)$, the eventually outward condition is not necessary.

Locally finite-dimensional infinite Gabriel theorem conjecture. The category $\operatorname{Rep}_{\mathrm{lf}}(\Omega)$ is of unique type and is infinite Krull–Schmidt if and only…