Germ representability and local integration of vector fields in a well adapted model of SDG
type: Item
instance of: scholarly article
title: Germ representability and local integration of vector fields in a well adapted model of SDG
zbMATH Open document ID: 0702.18008
DOI: 10.1016/0022-4049(90)90152-8
author: Eduardo J. Dubuc
published in: Journal of Pure and Applied Algebra
publication date: 1990-01-01T00:00:00Z
review text: The primary example of a ``well-adapted'' model of synthetic differential geometry is the topos G constructed by the author [Am. J. Math. 103, 683- 690 (1981; Zbl 0483.58003)]. There is a full embedding of the category of paracompact \(C^{\infty}\)-manifolds into G, which preserves transversal pullbacks and open covers. The article under review shows that the real line object R in G satisfies two additional axioms of interest: a germ representability axiom and an axiom for the local (infinitesimal) integration of vector fields. After reviewing the construction of G and some facts about Penon opens in G, the author proceeds to develop and prove these axioms. Some of these ideas are pursued at greater length in the author's joint work with \textit{M. Bunge} [Mathematical logic and theoretical computer science, Lect. Notes Pure Appl. Math. 106, 93-159 (1987; Zbl 0658.18004)].
Mathematics Subject Classification ID: 18F15
Mathematics Subject Classification ID: 18B25
Mathematics Subject Classification ID: 51K10
zbMATH DE Number: 4150469
zbMATH Keywords: local integration of vector fields
zbMATH Keywords: synthetic differential geometry
zbMATH Keywords: paracompact \(C^{\infty }\)-manifolds
zbMATH Keywords: germ representability axiom
zbMATH Keywords: Penon opens
reviewed by: K. I. Rosenthal
MaRDI profile type: Publication
full work available at URL: 0022-4049(90)90152-8
OpenAlex ID: W2005186074
cites work: Vector fields on \({\mathbb{R}}^{{\mathbb{R}}}\) in well adapted models of synthetic differential geometry
cites work: Q3807405
cites work: C ∞ -Schemes
cites work: Q3926774
cites work: Logical opens and real numbers in topoi
cites work: Q3223016
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description: scientific article; zbMATH DE number 4150469