8 problems

Let $X$ be a cellularly stratified space. Cellular sheaves and cellular cosheaves on $X$ are categories of sheaf-like and cosheaf-like data on the face poset of $X$, with morphisms…

Let $X$ be a space, let $NORM(X)$ be the site of normal coverings of $X$, and let $OPEN(X)$ be the standard site. Let $S$ be a set, write $S_{\#}$ for the associated constant coshe…

Let $X$ be a topological space, and let $\mathbf{CS}\left( X,\mathbf{Ab}\right)$ denote the category of classical cosheaves on $X$ with values in abelian groups. The non-abelianity…

Let $M$ be a manifold, let $l$ be a positive integer, and let $k_1,\ldots,k_l$ be degrees. For a cover $\mathcal{U}$ of $M^l$, suppose that every intersection of elements of…

Let $G$ be a locally compact totally disconnected group, and let $A$ be its closed central subgroup. Suppose that $G$ acts smoothly on a simplicial set $4\mathcal{X}_\bullet4$ of d…

Let $X^{et}$ be the étale site from Example, let $A$ be an abelian group, and let ${\Greekmath 0119}_n^{et}(X)$ and $H_n^{et}(X,A)$ denote étale pro-homotopy and étale pro-homology…

Cosheafification conjecture. There is a natural equivalence

Nadler–Tanaka's cosheaf conjecture. The functor