4 problems

The Generalized Pushout Conjecture. The following statements hold: first, the map $p:X\to X_+$ is a weak equivalence; second, given a connected diagram of controlled theories $J$,…

Let $\mathfrak{D}$ be a coherator for $\infty$-categories, and suppose it can be endowed with a system of inverses. A coherator is contractible when it is a coherator for $\infty$-gr…

A globular weak $\infty$-groupoid model is any of the unspecified models of globular weak $\infty$-groupoids considered in the conjecture. Let the category of such models be equipp…

Grothendieck's conjecture. The functor $\overline{\Pi_\infty}$ is an equivalence of categories.