On the role of quantum structures in the foundations of quantum theory

David Geoffrey Holdsworth

In this paper I shall outline a possibility for incorporating category theory in an essential way into the foundations of quantum theory. The role for category theory which I shall sketch here is strictly foundational in the sense that it offers no new perspectives for a physicist working within the quantum formalism, but rather provides a way of interpreting the algebraic structure by giving an alternative axiomatization of the underlying logic of the theory. The axiomatization is given without recourse to any classical set theory by invoking methods closely connected with the work of F. W. Lawvere. More precisely, then, a possible approach to the foundations of physics which axiomatizes its algebraic structure in a way which is independent of set theory and hence points, as it were, to a structuralist foundation of physical theories, will be proposed.

Théo Kahan, H. Ingram

Carl Friedrich von Weizsäcker

Pablo Reyes

This preprint presents the foundational structure of the Theory of Informational Selection (TSI), a framework that reconstructs physical ontology from correlational and informational principles. The work develops the concept of the Informational Totality, introduces the emergent geometry induced by Fisher Information, and explores the role of Quantum Fisher Information (QFI) as a partial experimental witness of the theory. Abstract: The Informational Totality is defined as the complete set of correlational structures that determine the emergence of physical degrees of freedom. This preprint develops the mathematical foundations of TSI, including the variational principles that govern informational selection, the geometry induced by Fisher Information, and the functorial formulation connecting correlational modes with emergent physical behavior. The work also discusses the role of quantum materials and collective electron states as potential experimental analogues for the emergent metric structure. The manuscript concludes with an outlook on future developments, including the extension toward cosmological regimes and the integration with quantum information theory. This document is the first formal installment of the TSI program and serves as the conceptual and mathematical basis for subsequent papers.

Waldemar Superson

GTi (Generative Theory of ilons) is presented as a foundational generative ontology underlying relational, structural, informational, and categorical approaches in modern physics. The theory replaces substance‑based primitives with ilons—abstract generative units related through morphisms in a small category. Informational and structural configurations ariseas colimits of realized diagrams, and a family of functorial invariants Θ,S,k,λ,χ captures structural properties such as distinction, coherence, stability, and topological class. GTi is not a physical theory but a pre‑relational substrate from which multiple higher‑level frameworks may emerge. It provides a deeper generative layer beneath relational quantum mechanics (Rovelli), informational ontologies such as Wheeler’s “it from bit,” categorical physics (Baez), categorical quantum mechanics (Abramsky–Coecke), ontic structural realism (Ladyman & Ross), and geometric or spinorial programs (Penrose). GTi also offers a structural foundation compatible with spectral and distinction‑based approaches. The article develops the mathematical foundations of GTi, including the generative category I, the realization functor G:I→Set, the role of diagrams and colimits in emergent structure, and the definition of structural invariants. GTi is proposedas a candidate for the deepest ontological layer beneath relational physics and other contemporary foundational programs. Author: Waldemar Superson

C. Piron