2001/11/06 by Kosta Došen, K. Dosen, Dosen, K.
Computer Science · Mathematics · #18A15 #18A40 #18D15 #Advanced Algebra and Logic #Category Theory (math.CT) #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #math.CT #math.LO #msc:18A15 #msc:18A40 #msc:18D15
paper · pdf · doi:10.48550/arxiv.math/0111061
15 pages
arxiv created 2001/11/06 · openalex publication_date 2001/11/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.