# Abstraction and Application in Adjunction

Source: [Abstraction and Application in Adjunction](<https://www.sota2.com/research/paper/68fa4cad1e209131ce94e419>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T08:53:16.845Z

Authors: K. Dosen

Published: 2001-11-06T15:27:10.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/math/0111061>)

[PDF](<https://arxiv.org/pdf/math/0111061.pdf>)