Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

1 results

  • 6 - Localization of Categories

  • Amnon Yekutieli, Ben-Gurion University of the Negev, Israel
  • Book:
    Derived Categories
    Published online:
    15 November 2019
    Print publication:
    19 December 2019, pp 146-164

  • 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.