arXiv:2403.17961 · v4

A categorical formulation of Kraus' paradox

首次提交 2024-03-13 22:48

版本更新 2026-10-26 19:34

雷达观测 2026-10-29 00:36

摘要

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.