---
date: 2022-03-19 18:34
modification date: Saturday 19th March 2022 18:34:46
title: presentable category
aliases: [presentable infty category, presentable, presentable infinity category]

---


---

- Tags 
	- #higher-algebra 
- Refs:
	- #todo/add-references
- Links:
	- [presentation of a category](Unsorted/presentation%20of%20a%20category.md)
	- [adjoint functor theorem](Unsorted/adjoint%20functor%20theorem.md)
	- [accessible functor](accessible%20functor.md)
	- [local objects in a category](local%20objects%20in%20a%20category.md)

---

# presentable category

![](attachments/Pasted%20image%2020220510155850.png)

![](attachments/Pasted%20image%2020220320040312.png)

![](attachments/Pasted%20image%2020220505190419.png)

![](attachments/Pasted%20image%2020220505191013.png)

A special form of the [adjoint functor theorem](Unsorted/adjoint%20functor%20theorem.md) when all categories invovled are presentable:
![](attachments/Pasted%20image%2020220505191201.png)