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What categories fibered in groupoids over $\mathcal{C}$ corresponds to stacks? A category fibered in groupoids over $\mathcal{C}$ is given by a functor $p_{\mathcal{F}}:\mathcal{F}\rightarrow \ma …

Consider the category of smooth manifolds $\text{Man}$. I quote from n-lab page: Manifolds are fantastic spaces. It’s a pity that there aren’t more of them. I understand that this category $\text{Ma …

Not sure how this would be received here. This question is about smooth partitions of unity. Let $M$ be a manifold. Consider an open cover $\{U_\alpha\}_{\alpha\in \Lambda}$ of $M$. A collection o …

Question is the following: Is the functor $H^n_{dR}:\text{Man}\rightarrow \text{Set}$ a sheaf with respect to open cover topology on $\text{Man}$? More generally, are cohomology functors sheaves in …

This is not a research level problem for sure. But, similar question was asked by some one else $2$ years back on Stack exchange has not received any attention. So, I thought it does not suit there …

This is not a complete answer, too long for a comment. If we start with an arbitrary site $\mathcal{C}$ and if we want to define the notion of a $G$-torsor over $\mathcal{C}$, then $G$ is not expecte …