Category Theory For Beginners: Kan Extensions
In this video we introduce, define, and describe how to compute Kan extensions. Together with adjoint functors, Kan extensions are some of the most powerful concepts in category theory.
Discussion of the adjoint functors related to dependent type theory can be found around
2:25:30 of
• Foundations 7: Dependent Type Theory
More details about constructing intermediary arrows for colimits in Set can be found here
• colimits in set 1
• colimits in set 2
The 3rd, 4th and 5th video in this playlist describe a variety of different structured sets
• Toposes - "Nice Places to Do Math"
My notes about Kan extensions can be found here
https://drive.google.com/drive/folder...
A discussion of how Kan extensions can be used to find adjoint functors can be found here:
• Kan to adj
The following videos describe more precisely how to find Kan extensions in general, when dealing with the category Set.
• Double speed Kan Extension 1
• Kan Structured Sets Explicitly 2
• Kan Structured Sets Explicitly 3