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6 - Localization of Categories

Published online by Cambridge University Press:  15 November 2019

Amnon Yekutieli
Affiliation:
Ben-Gurion University of the Negev, Israel
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Summary

In this section we take a close look at localization of categories. Let K be an abstract category (i.e. without any extra structure), and let S ⊆ K be a multiplicatively closed set of morphisms. The localization of K w.r.t. S is a category KS equipped with a functor Q : K → KS, such that the morphisms in Q(S) are invertible and the functor Q is universal for this property. We give a detailed proof of the fundamental theorem on localization: Q is an Ore localization iff S is a denominator set.We then prove that the localization KS of a linear category K at a denominator set S is a linear category too, and the localization functor Q : K → KS is linear.

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Derived Categories , pp. 146 - 164
Publisher: Cambridge University Press
Print publication year: 2019

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  • Localization of Categories
  • Amnon Yekutieli, Ben-Gurion University of the Negev, Israel
  • Book: Derived Categories
  • Online publication: 15 November 2019
  • Chapter DOI: https://doi.org/10.1017/9781108292825.007
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  • Localization of Categories
  • Amnon Yekutieli, Ben-Gurion University of the Negev, Israel
  • Book: Derived Categories
  • Online publication: 15 November 2019
  • Chapter DOI: https://doi.org/10.1017/9781108292825.007
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Localization of Categories
  • Amnon Yekutieli, Ben-Gurion University of the Negev, Israel
  • Book: Derived Categories
  • Online publication: 15 November 2019
  • Chapter DOI: https://doi.org/10.1017/9781108292825.007
Available formats
×