Horizon Problems and the Yoneda Constraint

Abstract

We develop a systematic analysis of horizon problems in physics from the perspective of the Yoneda Constraint on Observer Knowledge. In the Yoneda framework, an embedded observer accesses a total reality only through the representable presheaf, which determines the observer's epistemic position up to isomorphism but cannot determine reality itself when non-representable structure is present. We prove that all types of horizons---cosmological, event, Cauchy, particle, and Rindler---arise as accessible subcategory inclusions, and that the Kan extension deficit along these inclusions quantifies the information hidden behind each horizon.

Key Results

This paper applies the Yoneda Constraint on Observer Knowledge to provide a rigorous category-theoretic analysis of one of the deepest open problems in quantum foundations and gravitational physics.

The central mathematical framework involves:

• Measurement Categories: Observer-system interactions formalized as morphisms in structured categories
• Representable Presheaves: The Yoneda embedding maps each observer to their complete relational profile
• Kan Extension Deficits: Information loss at epistemic horizons quantified as failures of exactness
• Cohomological Obstructions: No-go theorems arising as non-vanishing cohomology classes

Full Paper

The complete paper is available as a PDF (33 pages) with all proofs, constructions, and detailed mathematical development.

The companion Haskell codebase implementing all categorical constructions is available on GitHub.

Series 1 Context

This paper is part of Series 1: Foundational Problems, a collection of six papers applying the Yoneda Constraint to the deepest open questions in quantum foundations, black hole physics, and quantum gravity. The full series is available in the yoneda-ai repository.