Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ ZENODOarrow_drop_down
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
ZENODO
Research
Data sources: ZENODO
addClaim

Löb, Duality, and the Logic of Self-Reference: How Categorical Proof Theory, Fibred Coding, and Profinite Duality Compose Into a Structural Account of Internalization

Authors: Saluca Agentic AI Research Team;

Löb, Duality, and the Logic of Self-Reference: How Categorical Proof Theory, Fibred Coding, and Profinite Duality Compose Into a Structural Account of Internalization

Abstract

A recurring structural motif in recent work across mathematical logic, category theory, and homotopy theory is the problem of *internalization*: how can a formal system, a geometric structure, or a logical theory represent, classify, or reason about itself or its own components? This paper synthesizes five specific findings from the recent arXiv corpus—spanning categorical proof theory, localic classification, duality for logical theories, operadic models of Teichmüller towers, and monoidal structures on dependent type theories—into a candidate reading of internalization as a multi-layered categorical phenomenon. The core thesis is a *heuristic reading, not a derivation*: these five findings each instantiate a common pattern wherein a "coding" or "classification" device (a fibration with code structure, a classifying localic category, a profinite duality, a modular operad, or a closed monoidal structure on theories) enables a formal system or geometric object to represent its own morphisms, proofs, or internal structure, and that the coherence conditions required for this self-representation impose recognizable algebraic structures—Frobenius, Löb-type modal axioms, profinite monoidal constraints—on the resulting objects. Primary categories of the corpus sources include math.LO, math.CT, math.QA, and math.AT. The falsification path for the central claim is explicit: if the Frobenius conditions identified in monoidal 2-categories [corpus:arxiv:2606.02046v1] and the code structures on fibrations [corpus:arxiv:2606.01165v1] can be shown to impose *distinct, incompatible* coherence requirements when composed, the proposed structural unity dissolves. All sources are preprints; no claim should be read as established beyond what the respective abstracts state. ---Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename.Cited arXiv preprints: 2605.20407v2, 2605.21323v1, 2605.22071v1, 2605.22571v1, 2605.24240v1, 2605.26972v1, 2605.27197v1, 2605.29921v1, 2605.30285v1, 2606.00952v1, 2606.01165v1, 2606.01466v1, 2606.02025v1, 2606.02046v1

Powered by OpenAIRE graph
Found an issue? Give us feedback