Causal Coverage in Ordered Locales and Spacetimes
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908603114323968 |
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| author | Heunen, Chris van der Schaaf, Nesta |
| author_facet | Heunen, Chris van der Schaaf, Nesta |
| contents | We develop relativistic causality theory in the setting of point-free topology by introducing a notion of causal coverage in ordered locales, generalising their canonical coverage relation to incorporate causal structure. This improves Christensen and Crane's construction of `causal sites'. We connect to sheaf theory by showing that causal coverages can be interpreted as a generalised Grothendieck topology, and the sheaf condition as a type of deterministic time evolution. To develop these notions, we introduce and study parallel ordered locales. Causal coverage naturally induces a notion of domain of dependence. Comparing the localic and curve-wise definitions in spacetimes, the localic domains strictly contain the classical ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17417 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Causal Coverage in Ordered Locales and Spacetimes Heunen, Chris van der Schaaf, Nesta Mathematical Physics Category Theory We develop relativistic causality theory in the setting of point-free topology by introducing a notion of causal coverage in ordered locales, generalising their canonical coverage relation to incorporate causal structure. This improves Christensen and Crane's construction of `causal sites'. We connect to sheaf theory by showing that causal coverages can be interpreted as a generalised Grothendieck topology, and the sheaf condition as a type of deterministic time evolution. To develop these notions, we introduce and study parallel ordered locales. Causal coverage naturally induces a notion of domain of dependence. Comparing the localic and curve-wise definitions in spacetimes, the localic domains strictly contain the classical ones. |
| title | Causal Coverage in Ordered Locales and Spacetimes |
| topic | Mathematical Physics Category Theory |
| url | https://arxiv.org/abs/2510.17417 |