3 problems

Let $\mathcal{M}$ be the subcategory of $C^n$-manifolds, where $n\in\mathbb{N}$ or $n=\infty$, consisting of all manifolds but only diffuse $C^n$-functions. Let the elementary fini…

Let $S$ be an infinite set, and let $f$ be a $\text{\bf Gen}[S]$-morphism, where $\text{\bf Gen}[S]$ is the subcategory of objects admitting a cover by open sets of cardinality at…

Let $\text{\bf Gen}$ be the category of topological spaces under consideration, equipped with its pseudoétale and torsorial topologies. The formal smallness conjecture. The pseudoé…