Kan Extension
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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.
Some useful tutorial on this subject
MathProofsable
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Richard Southwell on Kan Extensions
This video[1] is close to 6 hours of lengthy explanation. A large number of examples are presented in these hours. {{#ev:youtube|g_jEEwrpm9c|||||}}