---
date: 2022-03-23 18:58
modification date: Wednesday 23rd March 2022 18:58:44
title: triangulated category
aliases: [triangulated category]

---

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


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- Tags 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- #todo/create-links 

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# triangulated category

![](attachments/Pasted%20image%2020220323185846.png)
![](attachments/Pasted%20image%2020220323185855.png)
![](attachments/Pasted%20image%2020220323185905.png)
![](attachments/Pasted%20image%2020220323191626.png)

## Standard terminology

Thick, localizing, small, $k\dash$linear, exact.

![](attachments/2023-01-23.png)

Relation to tilting:
![](attachments/2023-01-23-tilt.png)

See [compact generator](Unsorted/compact%20object%20of%20a%20category.md).

Relation to [[full exceptional collections]]
![](attachments/2023-01-23-full-exc.png)
![](attachments/2023-01-23-full-exc-1.png)

## Multiplicative systems

Seem to be related to [spans](spans) and [correspondences](Unsorted/correspondences.md)!

![](attachments/Pasted%20image%2020220323190033.png)
![](attachments/Pasted%20image%2020220323190051.png)

## Exactness
![](attachments/Pasted%20image%2020220422221514.png)

## Thick subcategories and quotients

![](attachments/2023-02-26thicksubcat.png)