A categorical formulation of Kraus' paradox

Andrew W. Swan

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arXiv · 2403.17961

A categorical formulation of Kraus' paradox

Andrew W. Swan

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Abstract

We give a categorical formulation of Kraus' "magic trick" for recovering information from truncated types. Rather than type theory, we work in Van den Berg-Moerdijk path categories with a univalent universe, and rather than propositional truncation we work with arbitrary cofibrations, which includes truncation as a special case. We show, using Kraus' argument that any cofibration with homogeneous domain is a monomorphism. We give some simple concrete examples in groupoids to illustrate the interaction between homogeneous types, cofibrations and univalent fibrations.

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Andrew W. Swan. 2026-08-31. A categorical formulation of Kraus' paradox. https://arxiv.org/abs/2403.17961

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