The Principle of Methodological Transport in Univalent Foundations: A Philosophical Analysis Abdulla Kachkynbaev

Abdulla Zhaydarbekovich Kachkynbaev

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The Principle of Methodological Transport in Univalent Foundations: A Philosophical Analysis Abdulla Kachkynbaev

A. Z. Kachkynbaev

2025-10-13

https://doi.org/10.24108/preprints-3113778

This paper introduces and substantiates the "Principle of Methodological Transport," a meta-mathematical thesis emerging from Univalent Foundations and Homotopy Type Theory (HoTT). The author, posits that the synthetic identification of algebraic structures with homotopy types creates a formal bridge for translating mathematical problems and their proof methodologies between different domains. This transport allows for the replacement of complex or non-constructive algebraic arguments with more direct and inherently constructive homotopical reasoning. The principle is rigorously demonstrated through a detailed analysis of recent work by Buchholtz, de Jong, and Rijke. Their novel, constructive proofs for classical theorems—specifically that group epimorphisms are surjective and that the Higman group is non-trivial—serve as primary exemplars of this transport mechanism. The paper argues that this principle is a fundamental contribution of the univalent perspective, where constructivity arises as a natural consequence of a shift in mathematical viewpoint rather than as a stipulated constraint. The analysis also explores the philosophical implications, such as the nature of synthetic identification versus classical modeling and the ontological consequences of the Univalence Axiom. Potential future applications in fields like algebraic K-theory and quantum foundations are also considered.

Ссылка для цитирования:

Kachkynbaev A. Z. 2025. The Principle of Methodological Transport in Univalent Foundations: A Philosophical Analysis Abdulla Kachkynbaev. PREPRINTS.RU. https://doi.org/10.24108/preprints-3113778

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