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I want to show that if $X$ is a smooth complex projective variety, then analytification induces an equivalence of categories between algebraic integrable connections on $X$ and analytic integrable con …

Here's how the argument goes, thanks to @abx. $\operatorname{At}(M)$ is given by $\mathbb{C}$-linear endomorphisms $D: M \to M$ for which the commutator $[D,f]$ given by $[D,f](m) := D(fm) - fD(m)$ ac …

It is well known that the spin structures on an oriented surface (with boundary) $M$ are in bijection with the set of cohomology classes $H^1(M,\mathbb{Z}/2)$. By Lefschetz duality, these correspond t …

Is there any treatment on principal "categorical" bundles - principal $\mathbf{C}$-bundles, where $\mathbf{C}$ is some (topological) category? I know that one can define "categorical covering spaces" …

$\newcommand{\Aut}{\operatorname{Aut}}$Let $G$ be an abelian group. It seems to be a well-known fact (for example here) that $B\Aut(K(G,1))$, the classifying space of the topological monoid of (unbase …