2 problems

Atlas descent conjecture. The following conditions on $F$ are equivalent: (1) $F$ satisfies descent along atlases; (2) $F$ satisfies hyperdescent. In particular, the full subcatego…

Let $(\mathcal{C},\tau)$ be a site, let $\mathbb{A}$ be an augmentation category, and let $f\colon\mathcal{F}\to\mathcal{F}'$ be a map in $\mathbb{A}\textbf{-Pr}(\mathcal{C})$. A l…