Wigner's Friend and the Yoneda Constraint

Abstract

We provide a rigorous category-theoretic analysis of the Wigner's friend thought experiment and its modern extensions using the Yoneda Constraint on Observer Knowledge. The Yoneda Constraint---the principle that an embedded observer knows reality only through the representable presheaf---provides a structural resolution of the paradox by establishing that different observers' descriptions are related by non-invertible natural transformations. We prove the Presheaf Irreconcilability Theorem: the presheaves corresponding to Wigner and his friend cannot be related by any natural isomorphism, making their descriptions structurally incompatible.

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 (32 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.