Kan Extension
Kan extension is a universal construct of generalized data type defined in Category Theory.
Proposed Application
Conceptually, we can use Kan Extension to generalize logic gates, specifically, two inputs, one output gates.
There are a total of 16 possible 2-input, 1-output, logic gates. They should be generalizable and represented using Kan Extension.
One may want to read this paper[1] by Marina on representing concepts universally.
Some useful tutorial on this subject
It would be helpful to learn enough about Limit/Colimit, Adjoint Functors, and Dynamical Systems, before studying Kan Extensions.
MathProofsable
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Richard Southwell on Kan Extensions
This video[2] is close to 6 hours of lengthy explanation. A large number of examples are presented in these hours.
This is about the time he started to formally introduce Kan Extensions. {{#ev:youtube|g_jEEwrpm9c|||||start=13600}}
Left Kan Extension
This is about the time he started to formally introduce Left Kan Extensions. {{#ev:youtube|g_jEEwrpm9c|||||start=18729}}
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.
- ↑ Southwell, Richard (Jun 28, 2021). Category Theory For Beginners: Kan Extensions. local page: Richard Southwell.