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Abstraction and Application in Adjunction

K. Dosen
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Abstract

The postulates of comprehension and extensionality in set theory are based on an inversion principle connecting set-theoretic abstraction and the property of having a member. An exactly analogous inversion principle connects functional abstraction and application to an argument in the postulates of the lambda calculus. Such an inversion principle arises also in two adjoint situations involving a cartesian closed category and its polynomial extension. Composing these two adjunctions, which stem from the deduction theorem of logic, produces the adjunction connecting product and exponentiation, i.e. conjunction and implication.

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K. Dosen. 2001-11-06. Abstraction and Application in Adjunction. https://arxiv.org/abs/math/0111061

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