---
date: 2022-03-17 20:15
modification date: Thursday 17th March 2022 20:15:37
title: thick subcategory
aliases: [thick subcategory, quotient category]

---


---

- Tags 
	- #higher-algebra/infty-cats 
- Refs:
	- #todo/add-references
- Links:
	- [Balmer spectrum](Unsorted/Balmer%20spectrum.md) 
	- [triangulated category](Unsorted/triangulated%20category.md)

---

# thick subcategory

A subcategory of a stable $\infty$-category $\mathcal{C}$ is called **thick** if it contains the zero object, and is closed under the formation of fibres, cofibres, and retracts. Given an object $X \in \mathcal{C}$, we write $\operatorname{Thick}_{\mathcal{C}}(X)$ for the thick subcategory generated by $X$.

![](attachments/Pasted%20image%2020220323191522.png)

![](attachments/Pasted%20image%2020220323191549.png)