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Negation and Involutive Adjunction

2005/06/15 by Kosta Došen, K. Dosen, Dosen, K. +3
Arts and Humanities · Computer Science · Mathematics · #03F03 #03F07 #18A15 #18A40 #Advanced Algebra and Logic #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Logic (math.LO) #Syntax, Semantics, Linguistic Variation #math.CT #math.LO #msc:03F03 #msc:03F07 #msc:18A15 #msc:18A40

paper · pdf · doi:10.48550/arxiv.math/0506302

10 pages

openalex publication_date 2005/06/15 · arxiv created 2005/09/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This note analyzes in terms of categorial proof theory some standard assumptions about negation in the absence of any other connective. It is shown that the assumptions for an involutive negation, like classical negation, make a kind of adjoint situation, which is named involutive adjunction. The notion of involutive adjunction amounts in a precise sense to adjunction where an endofunctor is adjoint to itself.

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