Does anyone know if there is there a name for the idea that new concepts (such as negative numbers, complex numbers or type constructors in a type system) are only ever introduced into a preexisting "system" so that they can be eliminated later, after helping make some progress?
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Interesting, for me the dual is _the other side of the mirror_, whereas lifting is moving to a "higher" (more complex, with more properties, etc)
I think that the idea of a dual *became* a mirror for me, but back then, before I had an intuition, I found this lift explanation useful. The mirror doesn't give quite the same sense of it being "easier to move around" on one side than the other.
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It's like a magical place where things are different (the kicker for me was the duality in projective geometry) ¯\﹍(ツ)﹍/¯ The problem with lift is that lift(lift) should be id, but it's "the second floor"
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Yes, I agree... elevators have more parameters than we want in our analogy!
End of conversation
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