---
date: 2022-01-15 21:49
modification date: Friday 28th January 2022 18:30:23
title: Tannakian
aliases: [tannakian, "tannaka duality", "fiber functor"]

---

- Tags: 
	- #todo/untagged
- Refs:
	- [Tannakian categories](attachments/Tannakian%20Categories.pdf)
- Links:
	- [monoid](Unsorted/monoid.md)
	- [Serre functor](Unsorted/Serre%20functor.md)

---

# Tannakian

Idea: can reconstruct $G$ from $\Rep^\tensor(G)^\fd$.

For $G$ a [pro-algebraic group](Unsorted/algebraic%20group.md), $\Rep(G)$ corresponds to $\QCoh(\BG)$:

# Notes

- A **fiber functor** is a functor satisfying various conditions implying that it is [prorepresentable](prorepresentable).

![](attachments/Pasted%20image%2020220406001547.png)