3 problems

Let $\mathcal{C}$ be a locally presentable linear category over a field. An object is compact projective if it is both compact and projective, and $\mathcal{C}$ is strongly generat…

For a commutative ring $A$, let $A\textrm{-}\mathcal{CAT}^{Mor}$ denote the Morita localization of linear categories and let $A\textrm{-}\mathcal{AB}^{proj}$ be the subcategory of…

Path-category realization conjecture. For every spectroid $\mathcal{C}$, there exists a choice of $(\mathbb{X},\Gamma{/}{\sim})$ such that $\mathcal{C}$ is the $\Bbbk$-linear path…