3 problems

The cofinality conjecture. Precomposition with $F$ preserves marked $(\infty,2)$-colimits if and only if, for every object $d\in\mathbfcal{D}$: (1) there are $c\in\mathbfcal{C}$ an…

Consistency conjecture. It is consistent, relative to the existence of large cardinals, that there is $(\kappa,\omega_1)$-reflective forcing where $\kappa$ is the first $\omega_1$-…

Consistency conjecture. It is consistent, relative to the existence of large cardinals, that there is a weakly homogeneous forcing which changes the cofinality of the first inacces…