---
date: 2022-05-14 20:06
modification date: Saturday 14th May 2022 20:06:32
title: "Serre functor"
aliases: [Serre functor]
---

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

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- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- [suspension](Unsorted/stable%20infinity%20category.md)

---

# Serre functor

Def. A serre functor of a triang. cat $\cat C$ is an autbequivalence $S_{\cat C}$ such that
$$
\operatorname{Hom}(E, F) \cong \operatorname{Hom}\left(F, S_{\cat C}(E)\right)\dual
$$
functorially in $E, F \in \cat C$.

Use in [noncommutative algebraic geometry](Unsorted/noncommutative%20algebraic%20geometry.md):

![](attachments/Pasted%20image%2020220514200634.png)
![](attachments/Pasted%20image%2020220514200704.png)

![](attachments/Pasted%20image%2020221006003351.png)