Functorial Differential Spaces and the Infinitesimal Structure of Space-Time
Authors:
- Leszek Pysiak,
- Wiesław Sasin,
- Michael Heller,
- Tomasz Miller
Abstract
We generalize the differential space concept as a tool for developing differential geometry, and enrich this geometry with infinitesimals that allow us to penetrate into the superfine structure of space. This is achieved by Yoneda embedding a ring of smooth functions into the category of loci. This permits us to define a category of functorial differential spaces. By suitably choosing various algebras as “stages” in this category, one obtains various classes of differential spaces, both known from the literature and many so far unknown. In particular, if one chooses a Weil algebra, infinitesimals are produced.
- Record ID
- WUTa03f1bc1961f4fb3af61302bc386a7e3
- Author
- Journal series
- Reports on Mathematical Physics, ISSN 0034-4877
- Issue year
- 2020
- Vol
- 85
- No
- 3
- Pages
- 443-454
- Publication size in sheets
- 0.55
- Keywords in Polish
- funktorialne przestrzenie różniczkowe
- Keywords in English
- functorial differential spaces
- ASJC Classification
- ;
- Abstract in Polish
- Artykuł poświęcony jest teorii funktorialnych przestrzeni różniczkowych w obszarze geometrii syntetycznej z zastosowaniem do osobliwości początkowej w modelu Robertsona Walkera.
- DOI
- DOI:10.1016/S0034-4877(20)30046-X Opening in a new tab
- URL
- https://www.sciencedirect.com/science/article/pii/S003448772030046X# Opening in a new tab
- Language
- eng (en) English
- Score (nominal)
- 70
- Score source
- journalList
- Score
- = 70.0, 01-05-2022, ArticleFromJournal
- Publication indicators
- = 0; : 2017 = 0.700; : 2020 (2 years) = 0.742 - 2020 (5 years) =0.987
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- Uniform Resource Identifier
- https://repo.pw.edu.pl/info/article/WUTa03f1bc1961f4fb3af61302bc386a7e3/
- URN
urn:pw-repo:WUTa03f1bc1961f4fb3af61302bc386a7e3
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or PerishOpening in a new tab system.