A categorical formulation of Kraus' paradox
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913285981339648 |
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| author | Swan, Andrew W. |
| author_facet | Swan, Andrew W. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17961 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A categorical formulation of Kraus' paradox Swan, Andrew W. Category Theory Logic in Computer Science Logic 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. |
| title | A categorical formulation of Kraus' paradox |
| topic | Category Theory Logic in Computer Science Logic |
| url | https://arxiv.org/abs/2403.17961 |