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created: 2023-04-26T17:30
updated: 2023-04-26T17:31
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date: 2022-02-23 18:45
modification date: Saturday 19th March 2022 21:44:07
title: localization (category theory)
aliases: [localization (category theory), Dwyer-Kan localization, Bousfield localization, Verdier localization, reflective localization]

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Last modified date: <%+ tp.file.last_modified_date() %>


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- Tags 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- [saturated](Unsorted/saturated.md)
	- [combinatorial model category](combinatorial%20model%20category.md)

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# localization (category theory)

![](2023-04-26.png)

![](attachments/Pasted%20image%2020220519020439.png)

![](attachments/Pasted%20image%2020220505190814.png)

- Localizing at morphisms:

![attachments/Pasted image 20210505015835.png](attachments/Pasted%20image%2020210505015835.png)

See also [Bousfield localization](Unsorted/localization%20(category%20theory).md).

![attachments/Pasted image 20210603191026.png](attachments/Pasted%20image%2020210603191026.png)

![](attachments/Pasted%20image%2020220319214419.png)

Characterization of [accessible](Unsorted/accessible%20functor.md) localizations for [presentable](Unsorted/presentable%20category.md) categories:
![](attachments/Pasted%20image%2020220505191437.png)