---
date: 2021-03-25
tags: [ web/quick-notes ]
---


# 2021-03-25

## 00:08

What is a [Kan extension](Kan%20extension.md)? #todo 

- Kan extensions: 
  
  ![](attachments/image_2021-03-25-00-08-55.png)

## 00:09

- What are [derived functors](derived%20functors) in a [model category](Model%20category%20theory.md)?

	![](attachments/image_2021-03-25-00-09-25.png)

- What is a [Quillen adjunction](Quillen%20adjunction.md)?

	![](attachments/image_2021-03-25-00-09-48.png)

- What is a [Quillen equivalence](Quillen%20equivalence.md)?

	![](attachments/image_2021-03-25-00-14-31.png)

- What is an [infinity category](infinity%20categories.md)?

	![](attachments/image_2021-03-25-00-42-39.png)

- What is a [topological category](topological%20category.md)?

	![](attachments/image_2021-03-25-00-44-37.png)

- What does it mean for a category to be [enriched](Unsorted/enriched%20category.md)?

- What is the [homotopy category](homotopy%20category.md) of a [model category](Model%20category%20theory.md)?

	![](attachments/image_2021-03-25-00-45-13.png)

- What is the model structure on (differential graded) vector spaces?
	What are the fibrations, cofibrations, and weak equivalences? 

  ![](attachments/image_2021-03-25-00-47-16.png)

- What does an augmented algebra correspond to a pointed affine [scheme](scheme.md)?

	![](attachments/image_2021-03-25-00-49-25.png)

- How are initial and final objects defined in [infinity category](infinity%20categories.md)?

	![](attachments/image_2021-03-25-00-51-20.png)