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Let $X$ be a compact metric space and consider the sheaf cohomology group $H^1(X, \mathbb{T})$. From a class in $H^1(X, \mathbb{T})$, I can get a principal $\mathbb{T}$-bundle over $X$ and from this, ...

There are several approaches of increasing sophistication and simplicity to defining derived functors. I know of universal $\delta$-functors and Kan extensions along localizations. More definitions ...

Let $f\colon X\to Y$ be a proper continuous map of topological spaces which is a Serre's fibration. $X$ and $Y$ may be assumed to be locally compact, $Y$ is connected topological manifold of finite ...