2 problems

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Accessibility conjecture for models of appropriately nice PIE-limit 2-theories
An appropriately nice PIE-limit 2-theory is a two-dimensional theory whose models and pseudo morphisms form the 2-category under consideration. Accessibility conjecture. The 2-cate…
Conjectureopen2-categories accessible-categories limit-sketchesarXiv posted 2 days ago
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Weaker form of Shelah's categoricity conjecture for accessible categories
Let $\mathcal{A}$ be a nice accessible category with directed colimits having just one model of presentability rank $\kappa$ . Weaker conjecture. Then $\mathcal{A}$ must be categori…
Conjectureopenaccessible-categories categoricity model-theoryarXiv posted 2 days ago

Accessibility conjecture for models of appropriately nice PIE-limit 2-theories