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date: 2022-02-12 00:50
modification date: Saturday 12th February 2022 00:50:58
title: Serre-Swan
aliases: [Serre-Swan]

---

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# Serre-Swan

There is an equivalence of categories
$$
\Top\VectBundle\slice \CC \qty{\scriptstyle \text{Hausdorff}} \mapstofrom \Proj\mods{C^0(X, \CC)}  \qquad E\searrow X \mapsto \Globsec{E}
$$