Difference between revisions of "Kan extension"
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=Left and Right Kan Extensions= | =Left and Right Kan Extensions= | ||
There are two kinds of Kan Extensions, left and right. They may be compared to the notion of horizontal and vertical composition in [[Category Theory]]. | There are two kinds of Kan Extensions, left and right. They may be compared to the notion of horizontal and vertical composition in [[Category Theory]]. | ||
=Left and Right Adjoint= | |||
Left and Right Kan Extensions can be thought of as Left and Right Adjoint when the target is mapped by an [[Identity Functor]]. | |||
==List of Videos== | ==List of Videos== | ||
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[[Category:Kan extension]] | [[Category:Kan extension]] | ||
[[Category:Adjoint Functor]] | |||
</noinclude> | </noinclude> | ||
Revision as of 10:09, 19 March 2022
A Kan extension is a mathematical object[1] that can be used to represent concepts or ideas.
Left and Right Kan Extensions
There are two kinds of Kan Extensions, left and right. They may be compared to the notion of horizontal and vertical composition in Category Theory.
Left and Right Adjoint
Left and Right Kan Extensions can be thought of as Left and Right Adjoint when the target is mapped by an Identity Functor.
List of Videos
- Kan Lifts and Kan Extensions, Part 1
- Kan Extensions and Kan Lifts, Part 2
- Kan Extensions by MathProofsable
- Category Theory For Beginners: Kan Extensions
References
- ↑ Lehner, Marina (2014). "All Concepts are Kan Extensions":Kan Extensions as the Most Universal of the Universal Constructions (PDF) (Bachelor). local page: Harvard College. Retrieved June 28, 2021.